That's not exactly true ...
If there is room on the tender you can book a tender ticket without an accompanying shore excursion. We've done it. Some people on another board (whom and which shall remain nameless) questioned my veracity.
If you jump off at Playa, you take the ferry across to Coz. About 45 minutes, and I think it's $8. If the seas are a bit rough ... and they can be in the strait ... it can be a less than pleasant ride.
If you don't get off at Playa, the ship just goes to Cozumel port.
pamda -- CM FIrst-Time Cruisers Editor