Just my opinion when you use your water its your brew. Brew it anywhere else and it won't taste exactly the same.
Except that the OP was not about results, but about recipe.
Certainly when you brew it, its your beer.
But if you brewed Denny's BVIP or Papazian's Goat Scrotum Porter, the recipe was theirs and the beer is yours.
If you looked at their recipes, among others, and crafted one of your own, or adjusted their recipe to your tastes/ingredients/equipment then it might just be yours.
So when does the recipe become yours, is the question I believe was asked.
It's more than just brewing it, but there's also a continuum from theirs to yours. Unless you crafted the recipe on your own.