For BSA concerns, if your policy and procedures allow it, it's not illegal or a regulatory violation, but if the procedures are counting bankers on meeting the customer and comparing their ID to their face, for instance, you're probably violating your procedures. If bankers are allowed to open accounts without ever meeting a customer, the appropriate process should be documented in CIP procedures. Since the BSA Officer is the one with concerns, and they're presumably the one who is conducting any related risk assessments and writing any related procedures, I would expect BSA examiners to have concerns also.
I think there may be a number of other concerns with having bankers accepting cash off-site and bringing them to the bank that aren't BSA related that should probably be explored. I'm sure there are contributors here who may be able to speak to whether, at some point, those deposit accepting bankers are considered a mobile bank branch and must be treated as such. Or maybe I'm wrong. I would still be concerned about the inevitable situation where a customer says they gave you $1,000 and the banker only comes back to the branch with $100.