So, I was thinking and realized that it's a pretty stupid way to use the Service Container, not really the way it's supposed to be. So what I did was this:

Rewrite the bindCLass() function:

	private function bindClass()
	{
		foreach ( \Config::get('social-auth.providers') as $name => $provider )
		{
			$this->app->bind('SocialAuth\\' . $name, $provider);
		}
	}

Now it binds all the providers into the service container.

Hence, here's the resolver inside the controller:

    private function resolve($provider)
    {
        $this->provider = \App::make('SocialAuth\\' . ucfirst($provider));
    }

Like this it all works and makes some more sense.