I'm not sure why the bartender would say Skyy Vodka, b/c unless they're falsely advertising their menu says another vodka. If you go to The Cheesecake Factory's website and their menu section click on "From the Bar" and scroll down to "Specialty Martinis" It says that they use Ketel One vodka.

SOUR APPLE MARTINI
Ketel One, Sour Apple Pucker and Midori