Unlike the rest of you, I am not trying to solve this case. I do like absolutes though, they separate speculation from reasonable assumptions.
I have to disagree with your conclusion. I think you're putting too much importance on the cards.* The biggest indicator is the D-rings or lack thereof. The D-rings are installed in the harness at manufacturing. It's not like someone would 'forget to include them'. If Cooper has any experience and knows gear at all, he most likely knows the difference between mains and emergency (bailout) rigs. He knows enough to ask for fronts and backs, and he knows how to put them on. And when he gets them he's not scratching his head trying to figure out how they attach, he knows that there are no D-rings. So he most likely knows that he does not have mains. Therefore they must be bailouts. There really isn't a third option.
I think he doesn't ask for more for the same reason he doesn't ask for a proper backpack. He doesn't want to waste any more time. He's going to make do with what he has and "get the show on the road".
*Packing cards - They are on reserves and bailout rigs for reasons previously described. The reason the military puts them on mains is so they can tell which loft and what packer handled them. If there is an issue in the field, they can backtrack where they came from. If a loft needs to issue a service bulletin or airworthiness directive, the people in the field can determine whether they have affected gear.