Cupcake wooden pick candles

Is it wise for a burning flame to be attached to something made out of wood?

If so, then this cupcake candle set ($3) from Celebrate Express is pretty darn smart. Each vibrantly colored wax cupcake measures 1" and, as you can see, is set onto a wooden pick of unknown length (I'm guessing about 2" or 3"). The probability of the picks actually catching fire is pretty slim, I'm sure, and a sliver of wood burning atop a birthday cake is hardly a catastrophe or fire hazard, but I'd still like to the see the back of the candle. Does the wick touch the pick?