Hmm, it seems that what "Antair headers" thinks is "full" isn't really full, as one of its reviewers noted and the screenshot confirmed over on AppWorld.
If I had access to a desktop email client when I needed to do that, I wouldn't be asking this question...
What I'm worried about is if those headers are actually stripped-off by BIS and not retrievable by anything on the BB. That would be a pity, but I guess it wouldn't surprise me if they are doing that to minimize the amount of data transferred with every email. That would seem to fit with their philosophy.
If so, it would be cool if there was something in the API that allowed you to retrieve headers when necessary.
Just to clarify: I'm a sysadmin and email administrator and when I mean "full" I mean everything: the full path from the sending device's IP down to where it got retrieved into RIM's network, the message-ID, the various MIME headers, X-mailer lines, return-path, bla bla bla..