And the FAQ also says that's unreliable. There are servers that say "sure, go ahead" for every address tested that way. And there are servers that say "no, we won't tell you, try sending first" for every email tested that way.

Hence, you'll get both false positives and false negatives for such an approach, and far greater than your true reality hits.

Hence, the FAQ's wisdom should be followed: you can't get there from here.