Let's review. A martini is made of gin and dry vermouth, garnished with an olive or a twist. At a stretch it is made of vodka and dry vermouth, but if you garnish it with an onion it's a gibson.
Now, as far as I can tell, the common ingredient is vermouth. So maybe vermouth is the necessary condition to create a martini. (This also makes sense because Martini & Rossi makes vermouth.) We do not, for instance, call a gimlet a "lime martini."
So why is pucker and vodka called an apple-tini? Why is any vodka-based creation of a bartender's fevered imagination called the "fevered imagination martini?"
Vodka does not make a martini! I'm not even willing to admit it's a martini if you add vermouth, but I'm damn sure that just vodka (plus whatever sissy fruit juice you add) does not qualify something as a martini.
That's right. I'm a purist. Go soak your head.