Perhaps. All I can say is I was told that too; I tried that; and it really, really didn't work out. I think I might have been more successful had I focused on my own interests more. Certainly looking at my career in my adult life, almost all my biggest successes, with maybe one exception, were when I chose what to work on instead of agreeing to work on someone else's idea.
Of course you do need to adjust this for your field. If you're working in pure math or Roman history, it's not all that hard to do your own thing. In experimental high energy physics, maybe not so much. If you need a million dollar laboratory to get started in a field, then you may not have a lot of choice in what you work on. Though even in the experimental field I'm most familiar with, observational astronomy, it still appears to me as if the most successful people did their own thing. It probably does matter than in astronomy, it's standard practice to allot telescope time based on proposals rather than ownership.
Also, of course, if you can decide early on your area and aim at the program that does that well, then that's the best of both worlds. If you know you want to work on high temperature superconductivity, you're better off in a department that does a lot of work on solid state physics and better yet superconductivity specifically rather than one that specializes in string theory or experimental high energy physics.
There was some support for the idea of starting an advice repository for grad students much in the same tradition as the Boring Advice Repository and the Solved Problems Repository started earlier by Qiaochu_Yuan. So here goes.
Please share any advice, boring or otherwise, for succeeding at grad school. I realize that succeeding might mean different things to different people, but I believe most people largely agree with what it means in this context. Feel free to elaborate on what you believe it should mean, if you have views on the subject.
I am a theoretical physics grad student, so I'm personally more interested in advice for mathy disciplines (i.e. physics, math, CS), and I also suspect that there are many grad students from these disciplines on LessWrong; but advice for any discipline is welcome as well.
Advice is welcome from anyone, but please do mention your background for providing the advice so that people can weight the advice accordingly. For example, I would be more be open to listening to advice from someone who has completed a very successful PhD, than from someone who has simply interacted with a lot of grad students but has never been to grad school.
Also, feel free to link to advice from other sources, and maybe quote the most useful parts in what you read. Remember, this is meant to be a repository, so that people can come and find the advice, so don't worry if it seems to be something most people would've already read or known.
Thanks!