While in the vast majority of cases I haven't encountered problems I have certainly come across the occasional lounge receptionist who seeks to apply their own rules of entry where this situation arises. IME it's more of a problem entering BA lounges with AA status than it is the other way around.
I can think of 1 location I visit regularly where a particular individual insists that it isn't within the rules. On those occasions I have always successfully argued that they are incorrect and gained entry but I dislike having to do that.