To me, there seem to be two issues here.From my point of view, the issue is of timing.
If it is established that the sister is a chambermaid of the mayor, and then later the party needs to sneak inside the mansion, that's fine.
If the party needs to sneak inside the mansion, and the heretofore wholly ignored sister suddenly becomes the mayor's chambermaid that is an issue.
Why? It's obviating the problem rather than solving it.
One of them is technical: most versions of D&D have no way of answering the questions Is my sisters a chamber maid of the mayor? Can she leave the side gate open for us? except by ad hoc table consensus. (Exceptions: AD&D OA Yakuza class; 4e skill challenge with a Streetwise check.) And ad hoc table consensus can have an element of instability as a method of establishing the shared fiction.
Still, the issue of settling where a PC's sister works, which - given the lack of mobility of employment in the typical D&D setting - seems like it will only ever come up once or twice - doesn't seem to me all that destabilising, even if it does require consensus to be reached.
The second issue is the one that puzzles me: I don't see how it actually hurts play for the players to get into the mayor's house via a side gate the sister leaves open. At the table, discussing all that and sorting it out probably takes 10 to 20 minutes, which is not wildly different from how long it would take to resolve a reaction roll to a bribe, or a thief's Climb Walls check followed by throwing a rope over for their friends. Thinking of the family member possibility doesn't seem any less clever, or any less interesting, than thinking of sneaking in over the wall. @Remathilis already pointed out that if the issue is resource consumption, the GM can easily frame it so the sister needs a pay-off of some kind roughly equivalent to whatever other resources might be consumed (for PCs greater than 1st level, in most versions of D&D, the resources to sneak over a wall are pretty cheap).
To me, it smacks of a GM determined to stick to their preconception of how play should unfold. Which takes me, again, back to @Hussar's point: under those circumstances, what reason do players have to take the setting seriously as anything other than a complicated puzzle-box? And if it's a complicated puzzle-box, why would they bother thinking about family, friends etc for their PCs?