I'd have to say, first to make it to the pros, the athelete is above the average in physical shape and capability. Since they have been doing this for years, (high school, college,) they are more resistant to injury than most, and have a natural recovery ability. It would be hard to argue genetics and conditioning do not play a key role. They have access to state of the art, cutting edge and often experimental forms of prehab, rehab and recovery. Teams have full time trainers, doctors, surgeons, massage experts, physical therapists, etc, whose only job is to make sure that the athelete is healthy. Resources are virtually unlimited. They get treatments that us common folk have hardly heard of; oxygen therapy, hypobaric (sp?) chambers, and who knows about the drugs. Top level atheletes are not always fully recovered. These guys play with pain. I would guess it is a mixture of pain killers, toughness and the almighty dollar that keeps them going. Well, those are just my theories. I'm no expert, so I am open to flames and arguements.
I think you are on the ball here. The only thing that I would add as well is time. Without 'standard' 40 hours per week jobs many pro's generally have a lot more time to devote to active recovery, seeking out alternate recovery methods and rest.
Many of those guys retire with severe injuries that will limit their mobility for the rest of their lives. Corticosteroids and pain killers can decrease pain in joints and allow them to keep playing in spite of an injury. That doesn't mean they aren't injured or that they aren't making the injury worse by playing on it. The general attitude is this is what they are played to do. No one cares if they can't walk well by the age of 45 because they will at least have some money to fall back on.
I've heard (though I would be interested to see how effective it is) that at one point a few years ago the popular thing was to sit in a room full of O2. Expensive, and I doubt this is the answer you are looking for, but I present it for discussion nonetheless.