This doesn't definitely prove that all the Death Eaters were half-bloods and such, but this line suggests at least two things: every wizard has some Muggle blood in their family line or many of the Death Eaters, like Voldemort, didn't make their heritage public knowledge; the assumption became that they're all pureblood because they killed everyone else and the most visible Death Eaters were purebloods. It's the same deal with Hitler being partially Jewish (I know that one is ALWAYS used, but it's a great example of the point I'm trying to make).
DH (American verision) page 574:
"Alecto, Amycus's sister, teaches Muggle Studies, which is compulsory for everyone. We've all got to listen to her explain how Muggles are like animals, stupid and dirty, and how they drove wizards into hiding by being vicious toward them, and how the natural order is being reestablished. I got this one," he indicated another slash on his face, "for asking her how much Muggle blood she and her brother have got."