I assume you mean TurnITin... probably a typo. I agree with you that Google can be used as well, provided it has been submitted to a Internet site. But, a student submission -- let us assume it is original and has not been submitted to an Internet site; it will not be be detected as plagiarism if another student copies parts of it and this version is checked for signs of plagiarism.
I have had a student who submitted an assignment, and I could immediately see that it was NOT her work; the use of the language could only have come from a native speaker of English but the student was Dutch speaking and her English language skills were not particularly good. I complained. The institution has a local variant of a plagiarism checker and I was asked to submit the work to this tool. It showed no evidence of plagiarism. I then sent it off to a lecturer who teaches academic English at a department of languages at a university, and he said it was not the work of a Dutch student. I then sent it off to an American lady who also happens to teach English and she came back to say that the writing was from the pen of a native English-speaking person, as I had suspected.
Users of plagiarism checking tool should be aware of the context when undertaking plagiarism checks. That said, some of the other tools can be very helpful. I have no experience of ITHENTICATE... others might well be able to report on their experiences.