This was the "trick" that caused Lady Doyle to nearly faint and further convinced Sir Arthur Conan Doyle that Houdini must be supernatural. What other explanation could there be!? Marcet Halderman-Julius in the magic journal Halderman-Julius Monthly recalls, "I could almost have sworn I heard a brittle sounding snap as he broke it off and certainly should have been justified in swearing in any court that I saw that the first joint of Houdini's thumb entirely severed from the second."
This cops behind Harry seem to be accepting the trick for what it is; a bit of hokey fun.
Patrick Culliton in Houdini The Key devotes a chapter to the Thumb Racket, and notes that there was another more complicated effect utilizing a false thumb that Houdini could have used. Or maybe he was just damn good!