Closed in spaces would be more of a hazard because of carbon monoxide poisoning rather than a fire issue. LP tanks are actually quite safe. The only issue is when people leave them on and forget them. I once saw a video of a guy shooting an LP gas tank with an incendiary bullet, the gas did nothing but leak out. Rather akin to throwing a match into a cup of gasoline. That being said, a closed grill left on can easily catch anything touching it on fire.

God I'm glad I own my own home.