That makes a lot of sense...... ok, no it doesn't.
And boy did they do it quick! I think we would have kept Hitler's body for all to see.
In Islam, the washing of the body is very important - when it's done and when it's not done. It's not done when the dead body is that of a martyr that of a martyr - a Muslim that has died on the battlefield as a warrior of Islam. In fact, a Martyr is suppose to be buried in his bloodied clothes, which is something else the DoD didn't do - quite on purpose.
The DoD, in carefully washing the body by another Muslim, is - to many people in the Muslim world - keeping Osama from becoming a Martyr.