This is the case for every hosted mail solution in existence. And external hosting/procesing in the mail space is quite popular from mailgun to google apps.

So I don't view this as a major concern.

The fact that the maker of this API has a very fly-by-night looking website - that's more concerning. I'd very much like to have some good indicators of trustworthiness, and a good idea of who to sue, if things go wrong...