Collection Accounts

There are a few ways:
You can challenge any wrong info that is listed in the account. The company that placed the information has to prove the info is correct, if they can't, it must be removed. Often they ignore this and you will have to take them to court to force compliance.
Another way is if it is a valid account you can attempt to offer a pay for delete to the company reporting...they don't have much incentive however to do this and typically will only do this if the account is old and due to fall off the report in a year or two anyway.
A sneaky way to do it is to have a settlement agreement with the company that has a non-discloser agreement that states they may not talk about the account at all.....then you just dispute with the credit report company and if they verify, then the company has broken the contract and you can sue.
And finally..wait the 7 years for it to fall off.

Do 3rd party collectors actually agree to sign a non-disclosure agreement with debtors? Because this is more or less analogous of PFD which is probably extinct by now.

Sometimes they do...I don't think they realize that it means they can't communicate with the credit reporting agencies. I've had a couple that haven't said anything about it and some who have. Surprisingly sometimes I haven't needed it, particularly on old debt that will fall off in a year or three...the ones owned by a debt purchaser.

"Well, you can get paid and remove it from the credit file, or I can let it sit for another couple years and you get nothing." has actually worked for me a few times.

Sometimes I get them to agree to delete on the phone, while recording the call, then if they don't I threaten to sue them and use the recording as a verbal agreement....they have crumbled on that too, but I am in a one party state and I don't TELL them they are being recorded.

I think it is all hit and miss and maybe a little luck :) ...but I have definitely noticed that if you use the laws against them and even get a bit creative, they will generally delete to just not be bothered anymore.