The system relies on printing a code in yellow dots at the edge of the document - yellow chosen as it's not obvious in daylight, but clearly visible under something like red light. Take out the yellow cartridge & traceability isn't a problem as the dots won't get printed.
Or just buy a mono laser printer/copier.
Though obviously if you're wanting to print something colourful instead of a plain document this isn't workable.
To be honest this is only a serious concern if you've registered your printer & serial number *and* you're printing stuff that you might not want traced back to you.
Otherwise it would need someone to actually get hold of your printer to do the comparison check, in which case it's probably a bit late. And in any case comparison of print engine defects has allowed printer/document matching for years without needing deliberately hidden patterns.
In general terms I don't see this as a particular problem as it's something that *could* be checked, but in general terms can't really compromise privacy: how many times will you produce a document which is unattributed, that you don't want traced to you, that someone with the necessary resources would actually like to track back, and would cause you legal problems if traced?
The other interesting 'hidden' technology is the anti-copy patterns that are embedded in things like banknotes eg. 'eurion', which cause things like copiers to just refuse to copy the document. Not quite so sneaky because you can see it, and has the advantage of being easily duplicated allowing DIY copy protection on paper documents once you know the spec to follow...