It's not a myth, "bing" does means "sick".
It also means other things like "ice", but "sick" is the first thing that comes to mind, and in China this is especially a big deal due to superstitions. Naming things is very important here.
amusing anecdote: I remember a discussion about someone who wanted to name his shop 森林木 (three trees symbol, two trees symbol, one tree symbol) and everyone told him it was a bad idea and it would fail because the trees where getting fewer and fewer and that this name was an omen of bankruptcy, and if anything he should put it in the opposite order. (He ended up choosing a different name entirely)
Bing is a really bad name, even tho this had probably nothing to do with it's relative failure