I'm not an AP but to the extent I milk free play to subsidize, cover and/or make a few bucks it's all about maintaining the level of play. But once you are in the system and receiving offers you can maintain those levels more or almost entirely by using the free play as your bankroll and maintaining the levels by playing on off of what you converted the free play to. This doesn't mean losing the money you got from running the FP through once, but rather using what you won off of it to play more and keep your coin in levels up, leave with what's left and return. Use those leftovers some day when you need a few extra $ of your own to maintain your coin in level when you're not able to get enough coin in off recycling the FP generated cash to maintain your play levels. With discipline however, which I'm assuming the AP fellows have, you should be able to make a few bucks.
You have some crazy day where you gambled a lot and ran up a higher than normal coin in level and subsequently got higher offers? You can either use that to maintain your normal level of play, which will take your future offers down to your normal level, or leverage that to increase your normal coin in levels so that your normal offers start coming in as somewhat higher.
This doesn't work everywhere. Get a big win off of this exercise at some places and you'll see your future offers cut even though your coin in levels haven't changed (but you'll have the $ from the big win to console you). Other places will only go so high on their offers. For example, no matter how much coin in I get at CP in Vegas, my regular offers never go above $600 (I got $750 a while back that time when they sent everyone higher offers, I believe that was discussed here). Some places will also consider your comp use and gifts you pick up - like if you have comp points piled up and use them to eat or shop at their gift shop in a big chunk, or use your food offers, or pick up giveaways. I'm assuming that the AP fellows have a feel for all of this at the places they play.
But some places don't care. A couple places I have played at did invite only giveaways for play - like get $x in gift cards for every so many points earned over a period, or earn x points and get a big screen TV, stuff like that. Guaranteed items not drawings (I ignore those personally). There were a number of those where I got the item, earned a ton of points, won real money and left up to boot while playing to get the points, then a couple of months later got way higher FP offers and gift card offer giveaways (i.e. come in x day and get $x Shell card kind of thing) for a couple months because of that higher coin in visit.
But you can't in my experience just go run the free play through once and leave with what $ you make and continue to get offers. They'll eventually disappear. This is my experience as a regular player. The AP guys must know something though that there'd even be a market for player cards like discussed in that WOV thread on here where someone's daughter got scammed. If I know I'm not going to be traveling somewhere in the foreseeable future, I will do this because if I'm not coming back I don't care about my future offers, and just take the money in pocket and go.