You're correct. No company would encourage the bowler to use their bare hands (imagine the potential liability if they did) but people do it anyway, and then reach for a slice of pizza or french fries.
The spray covers a larger area (per spray), whereas the foam pretty much sticks where it lands. Either way can get all over your hands, I suppose, but I see it more with the foam because the bowler wants it to cover an area larger than when it's applied initially to the ball.
We probably should all take some precautions for our long term health, but to each his own...