There are general principles in the law that would say in this specific case, Google is making money off this arrangement, this arrangement is based on making money off of scanning emails, people wronged by this arrangement have a right to recompense, so follow the money, that's where the recompense should come from.
Companies cannot dodge liability for their actions by hiding behind third parties. Otherwise, the UPS or Fedex labelled truck that just ran over your kid would, every time, turn out to be a flat broke independent contractor Uber driver that all the other companies in the chain would point the finger at.