I apologize. I didn't read you post clearly. I don't think we know exactly when the allegation of rape was made.
The question has puzzled me for awhile.
The timeline reads like this --
1:49:00 DPD takes AV to mental health center (0:17:00)
2:31:00 DPD takes AV to Duke Hospital (0:42:00)
2:50:00 DPD changes incident report to include alledged rape (0:29:00)
Was -- (1) a physical examination made that showed rough sexual activity,
(2) were the results of that examination then reported to the accuser (perhaps in question format, such as "have you had sex with anyone tonight?"),
(3) and (with the police present and presumably having one existing charge of public intoxication against the accuser), does the accuser (perhaps wishing to avoid an additional charge of prostitution, or explain the evidence of the sexual activity to a boyfriend), only then claim rape?
It would be interesting to know when the police first heard the accuser claim rape (or, for that matter, it would be interesting to know whether the rape charge even originated with the accuser -- it could have originated with the examining nurse, been adopted by the police, and only adopted by the accuser after sobering up and hearing about it).