There isn't much to disagree with in the advice you have received; the practice is indefensible. However, my first bank had $12 million dollars in assets, I knew everyone who came through the door, I would have known and trusted the caregivers, and would certainly have known that Mrs. Gentry would never blame the bank for any alleged misuse of the funds. The problem is that it's not Mrs. Gentry the bank will be dealing with.
At some point, either upon her death or disability, others will be involved. If it's the son who moved away 20 years ago he has completely forgotten about the communal nature of a small town. It will be beyond his comprehension that you would do such a thing. If he's the personal representative of his mother's estate he will feel that he has no choice but to make a claim against the bank for the forgeries. The "character" issues you rely on every day in a small town play a lesser role when you are discussing the bank's business and setting an example for younger employees to follow.