It really is simple like that and a lot of people are already doing it. That's why the masters programmes at my uni (KTH) are crammed with mostly asian (China, Pakistan, etc) foreign students every year, coming here for a free (as in beer) and decent education. It's a pretty sweet deal of course and has caused some public debate whether this is viable or not, since it's all tax payers money funding it.
In one of my CS courses there was an african guy in his late 30's enrolled so I guess it's indeed possible to work something out.