It's true alright. The British did much the same. At the start, they built a fake city a few miles north of London and lit it up at night hoping the Luftwaffe seeing the lights would bypass London and drop their bombs on it.Funny story regardless if it is true or not.
The British after they discovered the ruse, were smart in letting the Germans continue to waste manpower and materials building the phony air base. Once the construction was completed the Brits decided to have some fun and drop the wooden bomb as a symbolic gesture of thumbing their nose at the Germans. ...What makes the story unbeliveable to me is that it doesn't make sense to let the enemy know, that you know, what they are up to.