According to that article, the tracking dots only apply for color printers/printouts, so they wouldn’t apply in GP’s scenario (out of color ink).
I doubt that tbh - the wikipedia article above shows Reality Winner got caught printing (presumably) black/white NSA documents because the printer was able to print the color tracking dots.
Therefore, not being able to display the dots shouldn't be an obstacle to the printer operating in B/W mode, as it would effectively be a B/W printer in that case. The more likely explanation is simply that HP wants to sell more overpriced color ink.
Interestingly, the Reality Winner documents were actually in color: https://en.wikipedia.org/wiki/File:NSA_Report_on_Russia_Spea...