I have to admit that I've never heard of this type of restriction. (But I also have to admit that I can't remember if I've ever asked for 5 or more keys before.) I do agree that if the hotel has rooms that accomodate more than 4 persons, then they should be able to make enough keys for each person.

My suggestion is to ask to speak with the GM to verify this restriction and to ask why they have that in place.