You are correct. Your question about their survival in areas where humans evolved is also very interesting. I disagree about Australia and possibly some other areas, though. There's strong evidence humans have been present in Australia for upwards of 60,000 years. That means they coexisted with the megafauna for at least 30,000 years. As for human presence in South Africa, mentioned in another post, this remains a very big and complicated ball of unwinding twine.
I still maintain there is absolutely no firm evidence for any of the three main theories: climate, human predation or disease. It's all just speculation.
I'm a little tired of humans being bashed as the cause of all worldly problems and disasters but I know we can be nasty customers, too. I think I view humans and human nature pretty realistically (I'm a conservative, after all). The American Indians used to hunt buffalo by driving huge numbers of them off cliffs. They used only a small amount of the meat and skins and left the rest to rot. Maybe the proto-Indians did the same with Mastadons and other large creatures. But evidence of the buffalo massacres exists. Does anyone know of similar evidence for megafauna? I'm not aware of it.
I located a couple of interesting sites that discuss the mystery pretty objectively:
http://www.cpluhna.nau.edu/Biota/megafauna_extinctions.htm
and http://www.austmus.gov.au/factsheets/megafauna.htm
If I had to choose one of the theories only I'd go with climate change. Animals adapted to glacial conditions probably didn't do so well in a suddenly warming world. But there are some hole in that theory too. It's an interesting discussion.
IMHO, those clovis-speared people didn't have the numbers nor mobilty to wipe out entire species of animals.
I go with climate change. Either a solar flare-up or a switch in the poles.