If you can approximate an algorithm with error that is "below the threshold that is considered acceptable in experimental measurements" (to quote another HN comment), then you have something as good as the algorithm itself for all intents and purposes.
Therefore the use of the word "solve" doesn't qualify as hype-rhetoric, and the distinction you're making does seem somewhat pedantic (even if technically true).
(I'm speaking as someone with only the tiniest amount of stats/ML experience, so I could be totally wrong!)