It doesn't really come down to trusting the Poker Site, for me I personally don't trust the Hardware, like Internet connection and computer even the Electrical grid, can fail at any point and cause you to lose money by shutting the game down.
Things like that don't happen at a live game, and even if they did I would still get my money back from a Casino if the Power went out. There are way too many things that are out of your control that could cause you to lose a game when playing On-line, I have been in some situations where I have lost connection while playing a crucial hand and it has cost me the game simply because I have not been able to click on the Call button.
There has been times when my opponent loses connection in a heads-up game and I only have to raise every hand to take the pot and eventually the game, Profitable for me but not the way I like to Win!