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Re:A SWAT team blew a hole in my 2-year-old son by ForHackernews on Wednesday June 25, 2014 @02:21PM (#7945808)
Interesting choice of example, as it happens there is in fact a "printer registry", where documents can be traced back to the device that produced them: https://w2.eff.org/Privacy/printers/docucolor/

(it's just that the average consumer doesn't know about it)

Re:A SWAT team blew a hole in my 2-year-old son by hga on Wednesday June 25, 2014 @02:33PM (#7945888)
There's a much tighter serial number system used for guns, all the way to a BATF Form 4473 (https://www.atf.gov/files/forms/download/atf-f-4473-1.pdf) that's required for the first retail sale.

To the extent there's any tracking of printers, it would at most tell you which store it was sold from, there isn't any required serial number recording done at checkout (well, as of when I last bought a color printer in 2006).

What you're referring to would be akin to comparing a bullet found at the scene of a crime with one fired from a seized weapon, albeit easier; a comparison system. Much less of a privacy concern, without any required "registration" involved.