I'm skeptical of a recipe that calls out its gin, but not its vodka, and also refers to a lemon twist as "a large thin slice of lemon peel." Not so skeptical that I won't try making it with several types of vodka. But skeptical nonetheless.
I'm now in an "americana" gin phase (st. george, distillery 209, etc) since they're not as commonplace here in Europe and I've been known to mix them with just commercial Vodkas whilst experimenting with a few cocktail recipes. I do that more with barrel aged gins -- the flavours of oily or smoky spirits don't easily work in cocktails so toning them down tends to produce some more interesting results.