I noticed that at least in my field, sometimes professors say to students, "send me the [research] paper when you're done with it, I'd love to read it [and give comments]". That is usually taken as a compliment that the professor is interested in the student's work, especially if the professor is famous.
Is it appropriate for students to say that to professors, especially if they're genuinely interested in the professor's research? Or could it be seen as pretentious?
For context, I'm a social scientist, and my discipline is not grant-driven at all, so it is very common for students to not work with their advisors on particular projects (e.g. they work with other graduate students, or other professors who are not their advisor)