Is it possible that this story is more to do with the acceptance or othewise of military ID cards being used as a means of identification. (It's difficult to imagine why this chap would have presented his card for any other reason). If for example he was paying by cash or a credit card that the company doesn't accept?
If this is the case it's entirely plausible and even, dare I say it, not unreasonable. I've been out for a year (almost) and IIRC there was talk of the introduction of joint ID card. I don't know if this has happened but if it has I wouldn't recognise it. I'd struggle with a RN or Army one for that matter.
Out here it's a passport or photo driving licence only.
Just a thought.