The mid-air collision was accidental; the story was revised to incorporate it.
The person jumping from one plane to the other is not Harry Houdini, it was a stuntman named Robert Kennedy (other sources say it was actor/stuntman Monte Blue). When news of the mid-air collision of the planes made headlines, Houdini cheerfully offered a reward to anyone who could prove that it was not him doing the stunts. Of course, he failed to mention that it really wasn't him performing the feat.