It's a lazy professor's way of doing his job. It isn't accurate and should never be taken as the gospel truth when reading a student's research submission.
This is spot on. Turnitin is the best checker, but of course, it can only be used at the time the paper is turned in (unless you pay for a subscription outside of work/school). Still, checkers are notorious for flagging common phrases and even worse for claiming a paper is plagiarized because it contains the same headers as other papers (which is often the case as students are doing the same assignment with the same questions and/or requirements). Using a program like Grammarly is okay for double-checking your writing style, but for an actual plagiarism check, it is quite unreliable. Nothing can take the place of simply citing properly, keeping direct quotes to a minimum, and double-checking your work and then checking again. We're all human and when we've been immersed in a project, it's easy to overlook the same mistake several times. During the writing process, our brain becomes conditioned to what we are thinking and not necessarily what we write. As such, if you meant to write "I will go" and, instead, wrote "I will got", your brain may be seeing "got" as "go". Worse, spellcheckers most likely won't catch "got" either because it's a valid word.
Also, time generally won't allow for busy freelancers, but if you can have someone else (a new set of eyes) proof for you, that's a plus!