Now Amazon isn't known to succumb to external pressure as far as I know. But depending on desperation and resources there's really a lot you could do. For example you could even go ahead and manufacture a controversy with some fake accounts and use it as evidence that Bitpatron is not doing due diligence. And of course, you could try to find another point of failure, like trying to convince their domain registar that the site is illegal. A lot of domain registars cave easily to pressure (Not all. Gandi is a good counter example.)
These aren't really theoretical attack vectors, but they are merely hypothetical for Bitpatron. Still, if you want something resistant to speech control you are gonna need more decentralization imo.
In neither case can I blame them. Those are fights which hurt them with very little upside.