OK,
No, you likely remember it correctly...that is still the problem with the FAA database, it allows for one runway endpoint. You actually have to induce a false runway within the FAA software if there is a displaced threshold.
Unfortunately, the navdatabase providers may or may not pick up a displaced threshold...so the FMC on the aircraft will not have the displ thres in the procedure.
I have many problems with the Jepp database in these regards, as well as others, as I can place a custom waypoint on approach, but not a custom waypoint for the runway.
Jepp is a competitor, they are not likely to listen.
(in regards to PSP, years ago, when in structural engineering consulting, the issue of the runway design for psp was one o my projects. it appeared that the new runway, at that time, (designed in the english/metric transition fiasco) the pavement thickness was screwed up as the contractor thought the thickness was inches, rather than cm...so the entire section is far to thin, hence the displaced threshold, given the lawsuits, I would have thought this was solved long ago, hence my surprise, when designing RNP to PSP, that the issue was still unresolved and there is 3000 feet of unused runway to date.)