[mattkrause]

This depends STRONGLY on the field and department.

Friends in math and political science certainly had experiences like the ones you described, but they would be fairly unusual in a wet-lab field, where students (and postdocs) are largely expected to work on an advisor’s grant. This is especially true when the experiments are expensive: a committee member would need to be generous indeed to put up tens of thousands of dollars for (say) an fMRI study.