In light of this recent incident - maybe Jenny simply left him. Maybe she didn't like him anymore. Maybe she's somewhere where the news of her being 'missing' hasn't reached her yet. Have they checked whether she used her passport out of Mexico? (sorry if this has been asked and answered already)
This is a huge part of the problem. The only things we know, except for an article (or two?) about her parents searching, are what JR says, often ambiguously; there's nothing from officials. For instance, this article says she never got on the flight to Cuba. It does not say how that was determined (would the airline tell him? does he have the ticket?) or provide any additional information, eg, the ticket has never been used, it was refunded, or it was changed to another day.
We haven't heard the normal things we'd hear early on in a missing person's case from officials or from family members. Many times when people have asked for more specific information or made reasonable suggestions on the Find Jenny page, their comments have been dismissed or even deleted. For example, volunteers spreading the word to Cancun, her next intended stop, via social media was firmly shot down as being "not relevant." It would cost nothing, hurt nothing, and possibly help locate Jenny, but somehow it's "not relevant."