If you think about it, a typical brick and mortar gets its money from hundreds if not thousands of customers every year (restaurant/cafe, auto mechanic, etc).
It's like renting a particular location: it's technically true that you could lose your lease, but that's only a risk to your business's long-term viability if your lease is artificially cheap (otherwise, you'll just move to another place on similar terms). And if your location is a particularly good deal, you should take it, even though losing it would suck.
Online, the same dynamic applies, but with lower transaction costs.
A customer is not necessarily someone who uses your product or service. That's a user. Think of a venn diagram....
The situation of startups who depend upon an external large business like Facebook, Amazon or Twitter is analogous to a car dealership that only sells one kind of car - say, Saturns. If Saturn stops selling to you or goes out of business, you're going to have to make some major changes.