House Mystery

My yard is surrounded by a four foot high fence.  The the house behind mine is undergoing renovation.  The back of my house is probably fifty feet from the fence.

The police determined that the molding through my back wall was scrap from the construction site, and the contractors said that the molding should have been in the dumpster. 

But they denied any knowledge of how the molding got from their site through my house.

The police theorized that some kids (this happened on the first day of school) cut through the construction site, picked up the molding, hopped the four foot fence, cut through my yard and slammed the molding through my outside wall.

Note that while one end of the molding is cut at an angle, the flat side is the side that was stuck through the house. 

It seems to me that if I wanted to vandalize a house by shoving a piece of wood through it, I'd use the sharp end rather than the flat end.

Also note that the molding went through the house 7' 6" above ground level, angled slightly downward. 7' 6" is approximately the outstretched fingertip height of a 6' tall person. Holding the molding clenched in one's hand and standing on the ground one would have to be well in excess of 6' tall to shove the molding through the house, though it's possible that someone stood on the fence and slammed the molding into the wall.

 It was stopped by a bookcase a few inches past the inside wall.

I doubt the police theory but I don't have an alternative explanation. Also note that the molding went through 2 layers of cedar shingles (which may have been somewhat brittle due to age), through 1/2" board (the house was built in the late sixties so the board is neither plywood nor particle board-- while particle board is made from wood chips and glue, this board appears to be made from sawdust and glue so it's not as strong as particle board), through fiberglass insulation and through the plasterboard on the inside of the house.

(a closer view of the inside wall)