It's like the facts are covered in clouds. There is a reason the banks offer incentives for tying together different account types.
The PROBLEM is - if you are on the edge just making your monthly payments and something happens to cause you to fall behind, that helpful institution may just help themselves. In many instances they have a right to offset your debt with your cash. Even if they make a mistake and you eventually get it corrected, you will be without those funds for at least 30 days.
The only certain way to protect yourself from this happening is to keep your cash (checking and savings) accounts in a different institution from the bank that has your auto loan, credit card, credit equity line, and any other obligations you've incurred.
[This discussion grew out of the previous blog warning of Wells Fargo and Wachovia's account freezing practices.]