That's a possibility. How probable is it, though? Seems like more of the exception than the rule to me and at that point if it does come up you have the choice of following the rules of the table or withdrawing from participation in the game. If you're not allowed a custom background I would expect you'll still have fun, but if not then no one can compel you to play with that DM in that game.
It falls into the category of
"what if?" ism. It's a condition being argued that has not happened and might not happen and you're arguing against what appears to be a remote possibility. I'd argue that the risk of a DM doing something we don't like or agree with is a risk regardless.
Of course, I could be wrong, but I would expect it more likely a DM will work with players to help with backgrounds than against them the majority of the time. I'd also point out that any background already in the PHB is permissible so being mechanically sound allows for free reflavoring. I don't imagine a DM is likely to say no to picking the mechanics of an existing background while changing it's name and flavor text to suit you're character better.
The backgrounds that could increase DEX for your rogue are: artisan, charlatan, criminal, entertainer, guide, sailor, scribe. soldier, and wayfarer. That seems like a fairly decent cross-section to me before reflavoring.
I hope you don't run into a problematic DM, but it doesn't look that bad from my perspective. ;-)