The main concern in software quality turning unknown bugs into known bugs, not with reshuffling the type and priority fields in a bug database (which is of course important).
"Zero bugs" means "exhaustively tested or else proved correct" (given a perfect set of high level requirements and detailed specification to begin with).
Any other use of "zero bugs" in a headline is clickbait.
The bugs that screw you are the unknown ones. Like security exploits that the Bad Guys find in the field before you do.