The cynic in me says that they don't want to avoid the US's surveillance so much as they want to insert their own. If it were another European country, I might assume otherwise, but Russia?
And why would Russia not be afraid of the NSA, after all they are a prime target.
But even now that the Europeans are fully aware of being spied upon by the US, they can not do anything about it without hurting themselves in the process. Europeans are weaklings, and not willing to endure the smallest amount of pain, even to avoid bigger pain down the road.