There are several modern escape artists who, when doing a straitjacket escape, lace the jacket with their arm slung up over their arm. In essence, they are half-way out of the straitjacket before the escape has even begun. This is by no means how one straps on a straitjacket, and it's certainly not how Houdini ever did it. Here is a good example of this modern-day cheat (identity of the performer concealed).
Now here are two shots of Hardeen showing how any self-respecting escape artist (or crazy person) wears a straitjacket. Arms folded. Of course, this makes it much more difficult to get your arms up over your head. But that's the whole point, isn't it?
Below is a publicity shot from the play Flim Flam: Houdini and the Hereafter, showing just how far this can go. Of course, this is a staged photo with actors and not a real escape artist, so it can be forgiven. Still. Let's be careful out there!
UPDATE: Here's magician Chris Cross doing a suspended straitjacket escape in Newcastle on August 28, 2016. No, this is not him in the middle of the escape, this is how he was put into the jacket. Dude...