24 hour fitness, as well as every other gym, allows you to train for the day for a price (usually between 10-25 dollars). You can walk into ANY gym in America and train for the day. HOWEVER, they make you sign a release that alleviates them of all responsibility if you get hurt. Thus, they would not let Phil train for the day without signing this release.
So, it has ZERO to do with liability. Something else happened and Phil Cheath is not providing the whole story.
I trained at a 24 hour fitness for the day, as well as other gyms (LA Fitness, Powerhouse, Golds, PF, etc).