I'll add my experience... And it is one that has historically been 50/50, without really any consistency even at the same location. What I have seen, however, is that the more "Aisle-y" the airport is, meaning, if it only has aisle cars and no true "reserved" parking spots, then the more likely they'll say "ok, grab a car in the aisle and have a good day" because thats pretty much their only inventory option... All the keys are in the cars. With that said, ORD is what I would consider "aisle-y" but there was a time the counter rep said "ok, go pick a sedan and bring back the keys so I can swap." Naturally, I ignored the word sedan and brought her keys to an Explorer Ltd. She apologized and asked me to get keys for a Camry or Altima instead. No more than 3 weeks prior at the same counter, another rep didn't even blink an eye with my full size Charger swapping out for a Grand Cherokee.
So again, as others say, this is definitely a YMMV thing. I'd wager that the rule book says you may only swap for the exact class car reserved, and anything outside of that is just a helpful rep at work. I base this on an experience picking up a car at New Haven, swapping out in Hartford. Despite Hartford having a full aisle lot, there was apparently only one Sonata they could swap me into.
If anything, I would guess the rental load for the upcoming day would also affect the request.