By the letter of the rules, a player could show up with a Background called "Brewer" that grants Perception, Stealth, thieves' tools, herbalism kit, and the noble's "position of privilege" feature. And, by the letter of the rules, the DM has no recourse without resorting to house rules.
The only thing this proves is that the rules are not a legal document, and that nobody should put any stock in the letter of anything. In practice, if a player truly feels entitled to exploit this loophole, the reasonable course of action is for the DM to kick them to the curb.