I don't know. There was a scrum and people pulling away what-looked-like-David screaming and what-looked-like-Syd, and for a minute there everything was upside down. It wouldn't be hard in that mess to have switched bodies, not minds.

The designers and production people have all said it's a mix. I think it's Wes Anderson time.

Sydney (inside David's body) is rescued by Melanie, Ptolemy and Kerry (David, inside Sydney's body, sees them drive up to the hospital). The switch back seemed to just happen after a time.
I don't understand the invisibility part, but I loved it.

Melanie, Ptolemy and Kerry drove up and rescued her. David first thought he remembered the Interrogator driving up, but later corrected it to Melanie.

They actually totally explained this, and it took two watchings and a good night's sleep for me to realize it—when David-inside-Sydney leaves the hospital, he sees three people get out of a car: the Interrogator, Ptolemy, and Kerry. Later he has to correct this memory to be Melanie, Ptolemy and Kerry. They look at…