I realize this is just a debate over a definition, so it's not very meaningful, but the fact is, you're on the wrong side of the common definition here. I just tested, and every spell checker that I just checked (Chrome, Firefox, MS Word, TextMate, TextEdit - perhaps some of these rely on the same underlying engine, I'm not sure?) accepts that sentence as not having a spelling error, so clearly there's some use for such a definition.
The grammar checkers, on the other hand, don't like it, but by changing "their" to "they're", they all accept it, despite the fact that it's still garbage. So don't overestimate how good "modern" spell checkers are...though there may be techniques to do a better job, they're not in common use, at least in the most common spell-checking contexts (which, lets be honest, pretty much means MS Word).