"The problem with Grand Unified Login Theory is that it often goes against the primary goal of having your own web service which is to build your own user base. In the long run your user base is worth more if it is uniquely yours as opposed to just being a subset of someone else's user base"

Why? The value of your "userbase" is not in your DB table, it's the users who interact with your service and arguably find it useful or fun. For many types of apps, allowing the user to interact with their friends is extremely important in achieving the above.

I don't really get your "flu" analogy, maybe you can say what you mean, are you literally worried about FB's downtime affecting your web service? that could be a valid concern for some web apps, I guess, realistically not for most.