I don't think that's it, madmucho. ISPConfig is geared to work with Bind9 whereas my servers are on Tinydns. So I set DNS to the servers by hand. So long as ISPConfig can then find where to send and listen, it doesn't seem to mind.
Also, every other aspect of mail works. If the MX record settings were wrong on the DNS servers, email would not work at all.
I suspect some kind of authentication or permissions problem here, but I am no expert, either.