First, I'd point out that something has probably already gone to the credit reporting agencies before you get a demand letter from a debt collector (the Fair Debt Collection Practices Act uses that term, rather than "collection agency"). So there's no real issue about your credit having been tarnished. That places you in a weaker position with respect to other lenders so they can attack you more successfully, so the first thing they do is to tarnish your credit.
The real question is whether you owe the money. The second question is who owns the debt. Second question first: if you have something in writing from the original creditor (caution, sometimes these letters are sent out by those who want to collect on the debt posing as the original creditor, so check with the original creditor to make sure it's valid if you get one), telling you to pay some third party, then you're justified in honoring that transaction. Debt can be bought and sold like any other commodity. Usually, though, the original creditor doesn't bother to inform the debtors because they don't want to go to the expense of proper notification, and having gotten the money they expect to get already, they no longer care about that. The problem for the consumer is that if you pay the wrong person, it's your tough luck - you could end up paying twice. Those who buy up poorly performing debt portfolios are usually in the debt collection business and are treated as such by the fdcpa. So unless and until you get something you can verify from the original creditor telling you to pay someone else, only pay the original creditor. You can't go wrong doing that, and the fact that you've paid is an absolute defense. If someone reports you to a credit bureau after you've paid, that's a violation of the Fair Credit Reporting Act and you should sue them. If the debt's been sold and you pay the original creditor, that's between the original creditor and the person they contracted with - not your problem.
Now the first question, whether you owe the money. If you owe the money and you can pay, pay the original creditor subject to what I said above. Use a payment method you can track, like a cashier's check from a bank - they often won't send a personal check back. If you get sued, you can have a subpoena issued to the bank to provide documentation you can use in court to prove you paid. Also send the check via registered mail return receipt required. If you don't get the green signature card back in the mail, complain to the Post Office and make them confirm delivery. (Some of these large institutions seem to have some kind of deal with the local post office such that they don't bother with signature cards.) You can send registered mail with a delivery confirmation, and I'd recommend that. You can also get a certificate of mailing, which you can use in any court in the U.S. to prove you mailed something. Have a witness document what you mailed and when you mailed it. You can't have too much evidence.
If you don't believe you owe the full amount demanded, but do owe something, pay the something with a written explanation of why you don't owe the remainder demanded. If you are paying in full, write that phrase, "payment in full" in the memo portion of the check. If they cash it, it's conclusive proof of satisfaction of the debt under the Uniform Commercial Code (which varies somewhat from state to state). Further, in many states, a valid good faith offer of payment in currency or something equivalent (such as a cashier's check drawn on a bank) is "tender of payment" and although that's not a substitute for payment, it means the same thing because the creditor made the choice not to accept the payment when offered (involves legal theories of "estoppel" and "waiver"). If you tried to pay and they wouldn't accept it, they can't come after you later on the theory that you didn't pay.
If you don't owe the money you can and should send a letter right away telling them so. If a debt collector gets involved, send them a demand for verification letter (you can do that even if you haven't paid in full, but don't owe the total amount demanded). I've posted an example of such a letter in another forum with suggestions for its use.
Ultimately, you may end up going to court. If you don't owe the money you can file an action for a declaratory judgment right away to protect your credit. It will be incumbent upon you to prove, by a preponderance of the evidence, that you don't owe the money. (Evidence generally means oral testimony under oath - documents and things introduced into evidence only support the testimony.) But if you're successful, you'll have a written order from a judge you can send to the collection agencies.
Or you can wait and see if they sue you. Meanwhile, you can do what you can to keep your credit untarnished by getting copies of your credit reports and sending the credit reporting agencies letters explaining that you don't owe the money and that the people who say you do are mistaken.
As to the issue of documentation - if you have sent a debt collector a denial of claim / demand for verification of debt letter pursuant to the FDCPA, then they have to send you something that meets the legal requirements for establishing that (1) there is a valid debt and (2) that you're the debtor. If they don't do that, then they can't take any further action to collect on the debt. That doesn't have anything to do with the documentation required to show that you should pay the debt collector rather than the original creditor. That should come from the original creditor, not the debt collector. If you owe money and a debt collector provides you with verification in response to your demand for verification, you can and should still pay the original creditor, not the debt collector, unless you've been told by the original creditor to do so. Note that one of the things the debt collector has to tell you in response to the demand for verification is the identity of the original creditor.
Most of the time, they use some kind of code that's not a valid name for any entity. I recently saw one that identified the creditor as "ATT WIRELESS SVC - 2 - 5GS" or some thing like that. That doesn't identify anyone. It has to be the true and correct legal name, which you can check on by calling the secretary of state, the state corporation commission, or whatever it's called, in the state where the creditor is chartered. As a hint, though, if it doesn't contain terms like "Co., company, limited, ltd., llc, lp, inc., N.A., or incorporated", it's not a valid company name. If the letter you get doesn't identify someone real, you can't possibly owe money to them. If they don't identify the original creditor in the response to a demand for verification, then there's no verification of a valid debt.
Ultimately, this process is governed by what people are willing to sue over and when they're likely to defend themselves in court. People who are in financial trouble are the least able to protect themselves. That's why tv-advertising tax lawyers like Roni Lynn Deutch can make so much money. It is my opinion that they can take the little money poor people have left, do nothing, and let the IRS grind the debtors up, and the lawyer will have gotten all the money, and done nothing to help the debtor who is left with no recourse because of his weakened condition.
I'm defending in a case right now where a credit card company says my client owes them money, but they have no documentation to show that he ever used the card, applied for the card, or requested the card; there's no written contract or agreement to pay interest. They file suit against such people because most of them will pay something without the cost of litigation, or if they go to court, they give up and get a judgment against them. Most people lose because they take the middle ground - but that's like Britian's policy of placating Hitler prior to WW II.
My suggestion, either protect your credit by paying what they want to the original creditor promptly, or dig in your heels and do what's necessary to protect your rights, and sue the debt collectors if they violate the FDCPA or the FCRA, even if (especially if) they're a law firm.