Having dealt with with Social Security, state agencies, and banks more than I'd care to, I would urge you to do the following:
1) Get a 100% clear answer on whether or not you are listed as "joint" or "authorized user/signer" for an account. This will probably require a call to the bank, but for less than an hour of you and your friend's time you will save yourself a whole lot of hassle.
The difference is like this: if you worked at a business that added you as an authorized user for a credit or debit card, this would allow you to use the card to buy things. But that doesn't make the money in the bank yours! On the other hand if you are listed as "joint", this regards ownership, and it could become tricky to establish whether its your money or not to any governmental satisfaction.
2) You are completely correct in being honest with the agency, but that's not enough - if you don't know what the facts are, you can't really be honest with them. If the form is unclear it's ok to ask, "on having a bank account, does being listed as an authorized user on someone else's account count if it isn't my money or bank account?"
But if you are listed as holding the account jointly, that changes the question to: "I am listed as joint on someone else's checking account, but it isn't my money - how is that considered?"
To Social Security it might mean generating an extra form, or it might mean you need to have the status on the account changed, or they might not care. But if you don't get the facts first, they won't give you the right answers or help you need.
And from personal experience, it's a heck of a lot easier to get a straight and clear answer from a bank than it is from a federal government agency. Have the facts with you when you contact them and you'll be ok - but trust me, you don't want them guessing!