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He's not pulling your leg, although I'm not certain that he is entirely correct that "all" printers do it. There is something called printer steganography that is used by many, perhaps most, printer manufacturers. This is a method of hiding information using invisible or barely visible dots. From what I understand, it includes things like the date the document was printed and the serial number of the printer, but it may vary by device. So if you go all Wikileaks, you had best be aware of it or you are going to leave a trail of little yellow printed bread-crumbs that could lead right back to you.
The Electronic Frontier Foundation has at least a partial list of printers that do/do not use the tracking dots.
I can't speak to the fit of your friend's tin-foil hat, but in 2004 PC World wrote:
"According to experts, several printer companies quietly encode the serial number and the manufacturing code of their color laser printers and color copiers on every document those machines produce. Governments, including the United States, already use the hidden markings to track counterfeiters.
"Peter Crean, a senior research fellow at Xerox, says his company's laser printers, copiers and multifunction workstations, such as its WorkCentre Pro series, put the "serial number of each machine coded in little yellow dots" in every printout. The millimeter-sized dots appear about every inch on a page, nestled within the printed words and margins.
"'It's a trail back to you, like a license plate,' Crean says."