Russia has always been about the Big man over the people kinda system, with the exception of Kerensky's 6 month government. Putin is the same self serving individual that Lenin, Stalin, Nicholas, Alexander, Catherine, etc all were, but each of those had to have a platform to stand on to say " hey Russia is a better place because I am in charge because X". Putin's illusion is the NATO push eastwards and has been very consistent in stating that. Everytime mainland Russian people are polled about the greatest fear for the Russian government it has been a high issue. I seriously doubt Putin really fears it because I believe his main goal in life is to alternate between being PM and president for life with his lapdog while ruling with an iron fist like the other Russian big men in history.
So no I don't believe we are directly the reason Putin came to power, but we sure allowed him a huge platform by NATO pushing aggressively eastwards. I still think we missed an opportunity while Yelstin was in power of probably having better relations with them.