This claim, mentioned in the title text of the most recent XKCD, is one that I've heard before.
The LEGO Group is already the world's largest tire manufacturer.
This time, however, I did some digging. Hitting up Wikipedia first, I found it references this article, which was posted on April Fool's Day of last year. (Possibly a coincidence, but it also has a few mistakes such as claiming LEGO is Swedish.)
I can trace the statistics it cites back to this blog post, but that's about as far as I can find with those numbers.
[T]he company that produces the most tires is LEGO.
Granted, it is comparing apples and oranges, but the claim seems to be that the number of little "tires" that LEGO makes is larger than the number of "real" tires that any tire company makes. Is that true?