I grill on my wood deck, I can't see how this could be a problem with a Weber kettle design, especially if you have an ash catcher. There's nowhere that a burning coal can escape. Just keep it reasonably far from the handrail and close the vents when you're done.
One problem I did have was when a red hot coal got stuck in a chimney starter and fell out as I moved it to the table, and burned about 1/2" through the deck. This was maybe the second time I used the grill and I've been paying close attention to the chimney ever since.
Added: I never leave it unattended for a long period of time, either.