So... Please explain it then. Or link to a document from the TSA that explains it.
Just because it's known by a lot of people doesn't mean it's not a secret. The ticket agent might not even know the full system, just what they have to do to get that frantic mom and 2 kids off their back.
Enter airport. Walk to departures agent of your airline and explain that you forgot your ID and there is no way that someone can bring it to you, or that you can retrieve it, in time to make the flight.
You get extra screening and a specially marked boarding pass and you get on the plane with everyone else.
My wife did this as recently as 12 months ago. SFO->MSP.
You know very well that that's not what "explain it" means. If you think the process isn't a secret, then find a document detailing the entire process, with specifics, end to end.
What happens in the extra screening? Is it the same throughout the country? What might vary in the process (YMMV, after all), etc.
You have a purely anecdotal account of what can happen at an airport that isn't even staffed by the TSA (https://www.flysfo.com/about-sfo/safety-security). What everyone else is looking for is a specific, detailed, transparent description of the entire process.
Just because it's known by a lot of people doesn't mean it's not a secret. The ticket agent might not even know the full system, just what they have to do to get that frantic mom and 2 kids off their back.