That’s me. I’m so annoyed at the New York Times. What kind of sentence is this?

The rift began in April when Katie put herself squarely on the side of “The Mercurys,” as that faction is known, on Oprah Winfrey, where she described how her talkative toddler turned unresponsive and out-of-control after his vaccines and only improved with unconventional, and untested, remedies.

On Oprah Winfrey?
Steadman goes on Oprah (presumably).
Guests go on Oprah Winfrey’s show, Oprah.