There's no technical reason I can think of for them adding a
DNS entry or mail configuration record for the domain if the
DNS is external to their network.
In many instances the "default" behaviour of the hosting control panel is to add either a
dns entry or a mail record for a hosted domain, however it should be possible for them to disable that.
This site, for example, sits on one server while its mail resides somewhere else. There is no issue with mail being sent from the server to my @irishwebmasterforum.com email as the mail server "knows" that it has to send it "offsite"
Hope that helps