In addition to PSA being so low, that a PSMA PET scan might miss any prostate cancers (as in your case), there are about 15% of prostate cancers that are “PSMA-negative” - they produce no PSMA such that a PSMA PET scan won’t see them, even though you know there’s a problem due to a rising PSA.

In those cases of PSMA-negative prostate cancers, the fallback is to use one of the older types of PET scans that aren’t reliant on PSMA - usually the Axumin PET scan or the C11 Choline PET scan (like Mayo Clinic uses).

If it were me, I’d get the other type of scan first before receiving radiation blindly, not knowing where the recurrence is.

The reason? —> Dr. Kwon (of Mayo Clinic) indicates that only 1/3 of men who have recurrence following prostatectomy have recurrence only in the prostate bed, and that they should not get salvage radiation there unless they’re absolutely certain of the location of recurrence. He says to first confirm where the recurrence is. (See Dr. Kwon’s presentation about recurrence: https://youtu.be/Q2joD360_pI). He talks about this topic specifically starting at about time 3:15 and ending at about time 4:35 of his presentation.

I think your doc is just following SOP here. In your case, he's probably reasoning that in all likelihood the recurrence is in the prostate bed - its likely spot. I'm assuming your pathology report after prostatectomy showed N0 for the couple lymph nodes the took out and microscoped. Guessing your doc based on experience w hundreds if your cases that he can try radiation alone and see what develops.
But there is literature out there about the efficacy using ADT in salvage radiation but I'm not sure it addresses cases w negative PSMA. You might check it out and then talk to your doc.