Just to clarify, graduate schools offering PhD degrees certainly do charge tuition that must be paid. The difference is that it is common, but by no means universal for the schools to provide graduate stipends that pay this tuition and often provide a living allowance. In exchange for this stipend, graduate students must work - being teaching assistants, work in a lab, etc. The source of this money is either the department where the grad student teaches, the lab where they work, or commonly, a mix of both.
MD/PhD students also are, in theory, responsible for tuition throughout the time they are in school. Again however, funds are available, usually via an NIH grant (MSTP or similar) to pay for this education so they don't have to pay themselves as well as provide a living stipend for them.