The segment also features Jim Steinmeyer, who wrote the definitive biography of Chung Ling Soo, The Glorious Deception.
Houdini and Chung Ling Soo (actually magician William Robinson) were close friends. In fact, the week Houdini had his career breakout at the Alhambra in London, Chung Ling Soo was on the same bill. Dot and Bess Houdini were also close friends. When Soo was killed doing the bullet catch in 1918, Houdini announced plans to do the trick himself. But he was talked out of it by magician Harry Kellar.
The True Nightmares episode is called "Too Rich, Too Thin" (Season 1/Episode 2) and is streaming at the Investigation Discovery website (the Soo segment starts at 18:15). It also repeats on the Discovery ID channel.