Given that Turnitin doesn't work as advertised anyway, I'm not really sure what the issue is. While it can certainly check all the internet sources, it fails to compare it to other submitted works. I know I've lifted sections from my own, previously submitted to turnitin assignments only to have it spit out 0% plagiarism when in reality I've only done half the work the second time around.
Hell, I know people who've lifted entire sections straight from Wikipedia, changed two words, and it detected nothing. The thing is broken, and I don't see why people still feel the need to bother with it.