I'm sorry, gentlemen, but this argument is moot.
As Tarheels has pointed out... Masters average means nothing. They may quit on you after a bad hole, etc, but they are not doing it to protect their average, imho. They may be, as Richard has said, "cherry-picking their rounds", but it's not for average.
Vanity? maybe. Boredom? perhaps. Frustration? possibly. Irritation? likely.
The solution? Don't play random games. Play with friends... join the ladders (www.WGTLS.co.uk)... even golfseekers... whatever it takes.
Remember this, in random pick-up games people will quit for whatever reason they choose... and there is nothing you, me, or WGT can do to prevent it. Don't put yourself in the situation to deal with these people... your blood-pressure will thank you.
Have a nice day...