Unless you lived right by, and I mean next door, to the refurb place I believe in Texas, it was never a few days. A few weeks maybe. I've had a Xbox 360 since launch go through 2 rrod's (so not really the same console) and at best it was 2 weeks to Georgia. They handled everything but shipping was never 2/3 day or better either way. I haven't had a return in 2-3 years now so maybe they got soooo good at the end that changed but I never remember it being that quick. MS also finally owned up to and corrected a serious design flaw. I don't expect the same from Sony just yet. You'll at least get them looking at it in the same manner initially. It behooves everyone for them to check it out and refurbish first, then just replace as they determine the root cause.
I must not play my 360 enough but I have one of the originalish white 360's bought at the same time as others (not day one, but before any of the fixes) and never had a RROD.
But now that I say that online watch it die the next time I turn it on. Glad I never had to send it in because Minnesota is a skosh farther than Georgia.
I live in Poland and had a white one RROD after about 11 months. Everybody told me: it'll take weeks. So I sent it in and went out and got myself one of the slim ones. Five or six days after a courier came to pick it up, another one came to drop it off. It'd go to Germany, been fixed and sent back to the Poland in under a week.
I forgot about that point. At some stage they would send you a refurb as you likely "proved" you sent yours in. They knew they would replace it so sometimes it would come back stupid quick. In all but the last of mine, I got the same unit back which likely accounts for the delays. They, and I as well, likely preferred letting us keep the same unit for warranty, live, etc purposes as the "move my stuff to a new Xbox" wasn't terribly fun to do, much less any more than once.