He probably would have booted me out and hired someone else willing to do the research if that had been the case.
If you've got a non-research source of funding like a fellowship or TA funding, by all means, have some fun.
But, if you're being paid from research funds, it's important to accomplish the research mission first.
If you have time left over, take some fun classes.
I disagree with this point. If you have an advisor encouraging you to keep your eye on the ball getting out frequent publications, you should be grateful. You certainly will be when you get your Ph.D. and have > 3 publications under your belt for your job search instead of 1 and "several in submission."
It is definitely the responsibility of a good advisor to make sure that their student leaves grad school well-prepared and with a competitive CV. An advisor who doesn't push his student to work hard and focus is surely doing a disservice. I just don't think that means the student shouldn't have a certain degree of freedom (maybe...10% of his time?) to pursue less immediately publishable knowledge.