You are correct, to a limited extent only. MMs make their money on a small spread in the buy / sell price. MMs buy shares for their own account. Once they receive a bid from a willing buyer, they may or may not sell, depending on the bid price. But if they do sell, they sell shares that they have already purchased for their own account. I.e., you do not buy shares directly from the original seller. You buy shares that were previously purchased by a MM.
How many shares to buy, if any, and at what price, is a key decision that all MMs have to make. But no one forces a MM to buy shares of anything. Stating otherwise is simply not true.
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