Stupid question, I know: Boxers vs. MMA fighters?

Your quite wrong. The MMA fighter doesn't move and just throw punches like a boxer does because it leaves you open to kicks, elbows, knees, takedowns etc. Also as soon as you watch a boxer go against someone who takes them down they lose straight away. Boxers don't wrestle so they have no takedown defense. So they will put on their back so fast they won't even realise until the ref jumps in because your choked out.