I think it does matter where you are staying. The price difference between agencies on a one day rental is MINIMAL, so truthfully, I wouldn't even factor that in. So if I'm staying at YC, why wouldn't I do a one day rental from Swan Dolphin - when I could be done with it in 20 minutes?
3 times I have called for pick-ups and only 1 time has it worked out and even then I ended waiting an hour past my appt time. If someone at the rental desk calls in sick, there are not going to be any shuttle picks up for a while, or if they get jammed busy - the shuttle pick up is last on the list.
Also, shuttle is a generous word, its a guy who picks you up in one of their rentals and drives you back to the rental desk.
That is why I asked "where are you staying?" A one day rental should have to all all that work.