I'm fairly certain that wouldn't be an issue. Relativity means that any (let's say non-accelerating, to keep us within the context of special relativity) reference frame is just as good as another. In the spacecraft's reference frame, it's chilling out, and a bunch of stars off a ways are moving really fast, but they don't really affect it.

It is an interesting problem though; I'm not really sure why it can't crush itself...