Jehovah's Witnesses are no more honest than anybody else...they just talk about it more. When they do the "right thing", they make sure to broadcast it because doing what is right isn't enough reward for them. I knew a good number of JWs who were liars, thieves, and cheaters, but were either deceiving themselves by justifying their actions or just didn't care, as long as they could fly under the radar.
One of the most dishonest people I ever worked for was a JW elder. He eventually was removed as elder after misappropriating monies people deposited with him to pay their electric bills. The interesting thing was that he was never disfellowshipped. Too many connections to make him a nice easy target for that. JWs are mostly bullies who pick on those who have the least power in the congregations.
As others have said, its a mistake to think that only JWs would turn this money in. There are many honest, trustworthy people in the world and they come from all nations and religious backgrounds.