IIRC, the DMV employees had to be trained (certified?) to process the Real ID apps, and no further checks are done (maybe only name match on the SS, but most in CA had already linked their SS to their DL). Years ago, I was part of a youth spoorts program, and we had do do deeper checks then, for any volunteers, and even deeper checks for All Star players. Thankfully, we had some "in the know" locally who were able to help (this was before the electronic methods they use today to try to deflect liability).
After all these years, I finally felt the desire to get my tribal ID. I had to send more information than needed for a Real ID. Of course, the tribal ID is also flawed, since in my case, it relies on the Dawes Roll, which has no real bearing to quantum, other than who was willing to sign up for the roll, and who was "considered" part of the tribe at the time. One side of my lineage did not sign up as they were afraid of the "federal men". I snicker when I see blurbs saying how "one drop" regulations are gone... (I prefer to think I belong to the human tribe, but as I get older, and worry about leaving family behind, there are available benefits - medical specifically - I cannot ignore.)
I know of some people who have had more than one SSN in their lives, for legitimate reasons, and sometimes there are conflicts which also proves the point there is no magic number or card which is infallible.
If you ever see a birth cert where the official signature (such as the MD) is typed, even though the requirement is for a physical signature, it does not mean the cert is invalid despite the requirement. Proves looking at a BC in its face is not enough knowledge to prove validity of the BC.