Chase Checking Acct and Credit Cards

Ok, here is a question I hope someone could help me with. I have been posting questions on here and everyone has been so great with their answers and advice. I owe Chase $10,000 in debt, have not made a payment for about 60 days, and was ignoring all their phone calls. With the advice on here, I called Chase up today, told them my unemployment situation and that maybe I could do a payment by next week. Here is the kicker. I bank with Chase and have a checking account and so he was able to see how much I owe and what I have in my checking account. He wanted me to give the "routing number" on my checking account and I said "no". He then said he has it anyways and they will post date a withdrawal of $300.00 next week. So I need to know if they are able to "butt in" and look at my checking account amount and can they take (garnish) any money out of it without me knowing? Should I close that checking account and switch to another bank other than Chase?