Rule #1: It's the student's paper, not the tutor's.
This is the most important rule of all. It's perhaps easiest to see and follow when the student argues a position I completely disagree with. My job is not at all to make sure the student has the right opinions; my job, rather, is to help each student express herself clearly, accurately, and thoroughly, regardless of what opinion she is expressing. (Of course, I have some subtle tricks, chief among them the exhortation to research, cite, quote, and rebut contrary opinions. I won't even suggest a student has the wrong opinion, but I can always help her become better-informed. Also, if I think a student has made an factual error, I will suggest that they carefully research and substantiate the statement.)
This rule is harder to follow, I think, when it comes to matters of rhetorical and expressive style. When the student's meaning is clear, but I think he is expressing himself awkwardly, I proceed with extreme caution. There are a few guidelines that are pretty solid — especially that the end of each sentence has the most impact — but a lot of cases are considerably uncertain. I will often just mark a sentence and ask the student what he thinks about it. If he seems uncertain or hesitant, I'll offer a suggestion, but if he pushes back, if he says he really likes the wording, I'll let it stand.
There are many cases, however, where it seems obvious to me that the student's writing should not be challenged. I remember one student who offered an interesting, if unusual, reason why she enjoyed a work of literature. She had seen another tutor, and the tutor had convinced her to change the reason to something more traditional. I persuaded her to change the reason back to the original. The student is offering her own reasons, not the tutor's. As a tutor, I will point out obvious fallacies, but beyond that, it is up to the instructor, not the tutor, to judge the quality of the reasons.
I exhort both tutors and students. To tutors, remember, it is your job to help the students write what they want, and it's a big enough job to help them write what they want with clarity. And to students, don't let any "expert", be it a tutor or Microsoft Word's grammar checker, tell you what you want to write. It's your name on the top of the paper, no one else's. No matter what the suggested change, make the expert justify the change, and if you are not convinced, keep it the way you want it. Even if it ends up being "wrong", it's better to be wrong on your own merits than right on another's.
