It's 'bug-free' in the same sense that qmail is bug free: you take a piece of software, design it very carefully to do only the minimum amount required to make it fulfill its purpose, spend a lot of time on making sure there are no 'bugs' under a very strict technocratic definition of 'bugs' (i.e., few features, slow running speed, idiosyncratic workings aren't 'bugs') and then make a career out of marketing yourself as being able to write 'bug free' code.
Of course to make the software useful in the real world, a lot of things have to be added to it - make sure to not include any of it in the 'core' otherwise the 'bug free' claim will go out the window really quickly.
So yeah, in that sense I guess it's technically (which I use as a euphemism for 'autistically') correct to call TeX bug free (the bounty program for bugs found in it is quite famous, and part of fore-mentioned marketing).
You think Donald Knuth has made a career for himself out of being able to right 'bug free code'?
Really?
He's made a career for himself out of being an extremely creative computer scientist and writing outstandingly scholarly books about programming. Far from marketing himself as producing bug-free code, he has published articles entirely devoted to the history of bugs found in his software.
(As for the bits that turn TeX into LaTeX, no one is making a career out of claiming that they are bug free -- for the simple reason that no one thinks they are.)
Of course not, it's hyperbole to illustrate the point. In the specific cases of Qmail and TeX, the 'bug free' aspect of it however is overblown and a marketing gimmick. It's not that hard (given enough time) to make something bug free, it's a whole different thing when the software needs to evolve at the same time to meet the (changing and expanding) requirements of actual users.
Actually, the reason for not evolving/rewriting TeX is so that old documents can be typeset and produce the same results. I find that an appealing goal.
TeX wasn't born in a night and suddenly appear in binary form. Knuth worked a hell lot to make it clean, make it work and make it fast. At least, for when he wrote it. Go and read The TeXbook
Of course to make the software useful in the real world, a lot of things have to be added to it - make sure to not include any of it in the 'core' otherwise the 'bug free' claim will go out the window really quickly.
So yeah, in that sense I guess it's technically (which I use as a euphemism for 'autistically') correct to call TeX bug free (the bounty program for bugs found in it is quite famous, and part of fore-mentioned marketing).