So according to this internal incident report which is never released (except you just did):
1. he deplanes voluntarily and unbloodied
2. he goes berserk in the terminal
3. he runs back onto the plane past the ticket agent
4. he then takes his seat back and the police materialize and order him off the plane
5. he calls his lawyer, no longer berserk, and calmly refuses to get off the plane Daily Wire
6. the police drag him out of his seat and he strikes his head
7. the passengers then video him being dragged out of the cabin like a sack of potatoes, bloodied
8. the passengers criticize the police for their actions
9. he then runs back on the plane a SECOND time, now bloodied, and hangs onto the curtain divider
10. he is removed again (no video, but presumably UA managed this as their employee reportedly boarded and took the still-warm seat)
11. the CEO of United accuses him of being belligerent
12. the dirt comes out on the doctor's history, but may be the wrong guy
13. despite the corporate push-back, UA loses the PR battle du jour
14. the CEO of United apologizes, abandoning the narrative he was pushing previously
The 'report' you cited only has him coming back on the plane once, but passenger videos clearly show him running back onto the plane, bloodied. That makes two times he gets past the UA agents.
But in all of this he did return to the plane.