Bs. That happens a lot and result in frustration and inferior research as the student keeps trying to fit everything into that little box of his interests.
I am just beginning my PhD but I have been "dipped" in academia for a few years and my short experience tends to agree with your point. It's not about loving your PhD project (although that doesn't hurt, and it should be preferred if possible) as much as it is about loving research as a whole. In my country (France) we have a lot of CS students doing "industrial" research (partially sponsored by companies) and while it couldn't be more dull, they usually do it because research is interesting as a domain in itself (and it pays well, without having to do any teaching).
BS. I think the opposite happens a lot: the student tries to "be interested" in what is hot or has funding/an interested adviser, they wind up unhappy and ineffectual because its all just pretend.
When you get a job and really get paid; you can be flexible with what you work on. When you go get a PhD, you should have some idea of at least the area you are interested in, you can be flexible within that area, but you should at least have one.