The most recent cup winners are Chicago, Los Angeles, Boston, and Pittsburgh. All of them made major moves prior to winning the cup.
Chicago acquired Hossa;
Los Angeles acquired Penner, Carter, and Richards;
Boston acquired Peverley, Kaberle, Seguin;
Pittsburgh acquired Guerin and Kunitz;
And that's just off memory, there's probably more. The point is, every single recent cup winner, no exceptions, had a pro-active GM. I bet the same applies to the Stanley Cup finalists, which doubles the sample size. A proactive GM is a requirement to a Stanley Cup.
Timmins is a great scout, but you can't win a cup by just giving Timmins 7 draft picks every year and hoping for the best. The good drafting has to be complemented by good signings and good trades. The idea of "building a winner through the draft" is something only ignorant sheep could buy into as a viable strategy in and of itself.