But the video you referenced described the printer imbedding a coded image on each printed page so that one could tell that the copy came from the printer rather than a government press. That's quite a different matter than the printer connecting to some government server somewhere and automatically reporting you for printing money.
Too many conspiracy theories on e-ham these days 
OK maybe I am creating the confusion, I thought it was making sense.
We have two different things happening.
1) When Money is inserted in the scanner/printer combo the scanner can detect it's money and reports the duplication to most likely the treasury dept or FBI. (That was the story I was told)
2) What Dave is showing is that a regular printout has information in it so they can trace it back to the Printer model, serial number and date etc. As he stated, most likely this is used in an after the fact case where they have a printed out Ransom note they are investigating or a document made by the unfriendly's that was confiscated during a raid.
It's not for checking if it came from a government press but to locate the exact person that made the printout. I would imagine the distributors are required to keep records of which store got which batch of printers, So that can narrow law enforcement's search down quiet a bit, some stores may even scan the printers serial number into their system when you buy them. That will give law enforcement the name and address of exactly who printed out that piece of paper.
The point I was making is that they seem to track everything that touches the digital world.
73s
Rob