Also the other hotel chains have (if it's a large corp) negotiated rates as well. When I worked w/ AT&T it didn't matter what chain I stayed w/, we had a corp rate. Same w/ the other F50 & F500 companies I worked for. So technically all the hotel chains are in the same boat. I don't see Marriott losing out to the competition based on corp rates (unless they did some lousy negotiating w/ the corp).
Again I think the amount of cheaters is miniscule overall, is spread among all the hotel chains, and those who do use codes they're not entitled to probably stay at different properties for the most part, so not sure an individual property really takes a large hit.
What I always found amusing was, when I worked for the big corps, even if I did find a better publicly available rate I was told not to use it, to use the corp rate instead cuz the corp had to hit a certain room volume to continue to get discounts. So I think Marriott & the other chains probably do ok - ie, it all evens out in the end.
Cheers.