I quess they did mention, that there are some people in a military without GC. How do they do it, I have no idea. One recruiter told me that there is no "legal" chance for a person without a CG to join the military. as of the executive order, it does not specify whether illegal aliens are eligible. I mean there aren't any direct words which indicate such possibility. The articles mentions the words of the few law professors who think that the language used in this order allows illegals to get naturalized based on it.
In either case, the sitution is a little bit messed up since it happens to hear about military personnel without GC while officially it should not be possible.