Then it probably doesn't matter if you resolve their DNS, because you won't be getting to any of their services anyway.
Several folks have mentioned that they don't see a problem with dns failure caused by an inability to reach all of the nameservers for a domain - because presumably clients won't be able to reach any of the hosts in that domain.
That's a wrong justification, not only due to the reasons you go on to cite, but because detecting a failure to look up a name takes a rather long time (your name server or resolver will typically have to rely on a time-out), while reacting to an ICMP Host Unreachable as a response to a TCP connection attempt is pretty quick (if your network is indeed off the net, but your DNS service isn't). This probably makes for easier debugging / better user reports, less of a "world wide wait", faster mailing list deliveries and probably also has other beneficial effects. Regards, - Håvard