[exim] MX record exists but exim says "HOST_NOT_FOUND"

I am having a problem with an exim setup on Debian etch. I have set it up as
a sending-only server (no local mail is delivered) but it is failing to send
mail for the local domain. This domain is "localnet" and is configured on
the internal DNS servers. On the machine is question, "dig -t mx localnet"
returns the correct mailserver, but "exim -d -bt toby@localnet" fails with
"DNS lookup of localnet (MX) gave HOST_NOT_FOUND" in the dnslookup bit

Does anybody know what's going on here?

Toby