that is HIGHLY incorrect. I have finished the medical quest for besty on MANY playthroughs after they had already been sent to forlorn hope
True, but there are a couple potential bugs that could be stopping the OP's progress on this one:
* Several users have reported that Corporal Betsy, if she is stationed at Camp Forlorn Hope, will only use a generic reply and not initiate quest dialogue. (This occurs when the quest is initiated while the recon team is still stationed at Camp McCarran and their help is used in the quest Three-Card Bounty, triggering their move to Camp Forlorn Hope, while the quest is still going on, before you have convinced Corporal Betsy that she needs help). A work around to this bug (PC only) is to enter the command "setstage 0015e480 10" to bypass the first stage of the quest. If you continue to experience difficulty increase the final two numbers by multiples of ten (20 then 30, etc.) to bypass each objective that cannot be solved by traditional means.
*Sometimes during the mission if you initiate a dialogue with Corporal Betsy but choose to tell her that Cook-Cook is dead before advising her to deal with her trauma, she will thank you and the dialogue will be over. When you try to initiate another dialogue with her you only receive a generic reply. The same thing happens if you quit the dialogue before you advise her to seek mental therapy; again, you'll be unable to initiate another dialogue.
...whether a patch fixed either of these, I have no idea.