I see your point, and I think that the guitar doesn't necessarily define your playing style by itself, but it does contribute to it to some extent. A Jackson KE-3 Kelly, for example, is designed for metal, so the various characteristics of the guitar will lead to a more metal-style "sound" in your playing; I mean, if you play reggae on a Kelly, it will still be reggae, but you might feel a bit more tempted to throw in some chugging riffs or needly-needly-needly bits ( :D) because of the nature of the guitar.
The great thing about Strat, Tele and LP style guitars, IMO, is that they're equally suited to all styles of playing.