Total nonsense of course.
A "browser" is a piece of "software". Pieces of "software" contain "bugs".
This is a law of nature.
To be sure some pieces of "software" contain more "bugs" than others, but a claim that any piece of "software" is "totally" free of "bugs", even if they're only claiming that it's "totally" free of the "security exploit" subset of "bugs", is, frankly, bollocks.