Academic researchers often pay either zero or get a massive discount on all kinds of stuff (hardware, software, data, samples etc.) for their research that people in private sector pay a huge premium for.
Not completely accurate. Every time you get a grant, your institution get a percentage of it to pay for indirect costs. These costs include office space, office personnel, and other expenses that the grant doesn't pay for directly. So, if you are getting "free" stuff from the department closest, it is very likely that your (or some else's) indirect expenses are paying for it.
Overhead percentages are set by each institution. My current one is set at 54%, meaning that for each $1 of award, I get to keep 64 cents and the university takes 36 cents (more or less).