But they were specifically worried about the transfers being scams -- at least, that's what they said. They insisted on calling my other bank to verify that I was in fact the owner of the other business account. And I know there's been a big increase in things like fake real-estate scams, so paranoia is understandable.
However, the way bank fraud/risk departments work is generally completely opaque. I've previously had Bank of America refuse to open an account, with no reason given and no possible recourse. And I can't imagine a much more vanilla, boring, good-credit person than me, so I have no idea what set them off!