What are you talking about? Everyone has to depend on some infrastruture to provide their service. I'd imagine pretty much every hosting platform (from amazon to dreamhost) has less reliability than facebook.
Also, reliability is one factor out of several, it is not the only, or even the primary, risk with using something like FB login.
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.
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.
You can packup your application and move it to Amazon/Rackspace/DigitalOcean, but if you use Facebook login exclusively or use a third party API for a core service and they decide to change (as GP suggests), you're fucked.