Rudy Giuliani has been fueling speculation that Hillary Clinton's health is not well. And Stephen Colbert thinks he may have discovered why the former New York City mayor may have some knowledge about women's bodies.

"I'm not surprised that he was able to diagnose Hillary Clinton so accurately without examining her," CBS's "Late Show" host said on Tuesday. "After all, Giuliani and Donald Trump are experts on female anatomy. It's true. Just look at this actual video the two of them made."

The show then played a video from the Inner Circle, a parody group that lampoons the current NYC mayor, from 2000. In it, Giuliani is dressed in drag and Trump hits on him. The scene ends when Trump sticks his face in Giuliani's chest in what's known as a "motorboat."

"Obviously, that's shocking," Colbert followed up. "And you're going to want to verify that video. Just go online and put down 'Donald Trump, Rudy Giuliani, drag queen, and motorboat'... Good, clean family joke,"

Colbert admits he doesn't think that's what Giuliani had in mind when discussing Clinton's rumored bad health, and then plays a news clip of conspiracy theories about possible illnesses plaguing Clinton. They include brain damage, Parkinson's Disease, autism, and even syphilis.

"Syphilis? You can not be president if you have syphilis. Just ask Benjamin Franklin," Colbert joked.

Watch the video below (at about 2:20 in):