It's not totally unsubstantiated, Tesla did post this:
https://www.teslamotors.com/blog/putting-tesla-hepa-filter-a.... Of course you should have a healthy degree of skepticism regarding tests Tesla did itself and maybe the numbers are massaged a little, but I doubt they'd straight-up lie. It seems like this test would be pretty easy to replicate by an independent source too, if someone wanted to try.
Edit: I did not see that there's already an entire HN discussion thread about this post: https://news.ycombinator.com/item?id=11617945 which discuss other possible weaknesses. Still, even with the usual HN nitpicking, I think it comes out pretty good.