What the fuck is your problem? I understand your unwillingness to open accounts for people who have a history of bouncing checks, as reported by ChexSystems. To a degree, I also get your reluctance to add someone with such a history to an existing account, even when the current account holder has a stellar record with you and every other bank they have ever used.
But where the fuck do you get off refusing to allow a current account holder in good standing to give such a person access to their safe deposit box? I mean, you’re not supposed to know what is in the box anyway, and it’s not like any of whatever is in there belongs to you. You’re not at risk, so what’s the problem?
Because of this policy, my money and my business will be going elsewhere. You may go fuck yourself with a barbed tetsubo.
Grumpy Bastard 
had to google tetsubo
Not a Larry Correia fan? Man, you’re missing out. (A tetsubo is the favorite weapon of one of the main characters in his Hard Magic series.)