Sovcit is lying.

There’s no goddamn way anyone let them on an international flight without a valid US passport.

It sounds like they do have a passport, but with a goofy signature because SovCit reasons, and they were trying to verify the signature using other goofy documents.
- Yeah, in many places you can file damn near anything you want at the County Clerk's office, especially if it purports to have anything at all to do with land ownership. They record things, but unfortunately for the SovCit, they do not actually confer legitimacy.
  I would just about bet that as the scammers who fleece the SovCits realized their market included certain people who somehow could afford to travel overseas, they needed something beyond the fake passports and the information about the n number of stars on passport CARDS for land crossings to CA and MX. I bet you can buy all sorts of information about how to get a real passport without selling yourself back to the "government".
Anything involving US, probably no, agreed.
However, I have been on 3 flights in the past 2 years which were international (albeit inter-european) where I wasn't required to show my ID even once.
Just thought it's kinda funny :D
- Border checks are an exception between Schengen countries.
  Airlines usually require valid id/pass in their terms. Usually only enforced to boot a few people off the plane when they're overbooked.

What is the 3 stars thing again?

It's absolutely nonsense. They're convinced a certain number of stars in the passport mean something, it means nothing.

Does anyone know what they mean about autographing something instead of signing it?

Word games to try and escape legal responsibility.
“That’s not my signature, it’s my autograph”
“Officer I wasn’t driving, I was traveling”

Amount of international flights I've been on so far this year: 20ish, I think
Amount if times someone cared about my signature: 0

Only time there has been extra hazzle was when the airline questioned my C1/D visa as I didn't work for an airline. Took them a while to realize that ships also travel internationally.

Oh, and there was this time I had one of those DE9-RJ45 console cables in my backpack, and I had to explain what it was for during a routine inspection.

I once bought beer with my friends debit card. This was back when you'd sign the receipt instead of doing NFC or entering your pin code. I signed it "Jesus Kristus".

Bartenders don't care.

It's nice to have insane people from Facebook who aren't schizophrenic or conservative.