Clearly not.

Same as when one of the big name hosting companies takes a site down. You hope it’s archived, and if it was important enough to you, hopefully you saved it to your personal server.

What you’re describing is a major benefit of federation. Any site can be taken down. But when a federated server goes down it’s because the site owner exercised their control over their own data. If Google or Amazon takes a site down, you lose your data, but they keep copies to use however they want.