Sure, but the more external components you tie in to the bigger the chance that one of them will be down. So you try to keep such dependencies to an absolute minimum otherwise you end up with the joint downtime of all those services.
It depends on your line of business, but if you compare the benefits of making user signup faster, lowering acquisition barriers and getting access to the social graph of users against the risks of depending on one of the top infrastructures in the cloud, I think it may well be worth the trouble.
Probably you are talking about redundancy where, I agree, it does go down.
As for which risk is the most important risk, well, that's up to your business to decide. But nothing is without risk, all you can do is choose which to expose yourself to.