If it wasn't in the film then it didn't happen.
The film takes place over a 25 year time period, beginning with the birth of Captain Kirk. During the film, we never saw Kirk use the bath room. Therefore, by your logic, Kirk (or any of the other characters for that matter) never took a dump or a piss. Then again, we never saw any of the characters eat, so they probably didn't need to use the bath room...