PhD programs in mathematics, statistics, philosophy, and theoretical computer science tend to give you a great deal of free time and flexibility, provided you can pass the various qualifying exams without too much studying.

Bolding the parts to which I object.

I have never seen anyone in a rigorous postgraduate program who had a lot of free time and could pass their quals without large amounts of studying.

Of course, I could just be, like magic, on the lower part of the intelligence curve for graduate school, but given that my actual measured IQ numbers are pretty in-the-middle for scientific academia (I won't tell what they are, though), and given that almost everyone else says they have little free time and have to study hard in graduate school, I'm inclined to believe the bolded phrases only accurately describe a narrow slice of lucky individuals.