I really think you're being disingenuous in this 'argument' and I'm about to say this fully aware it contradicts my own position on where we should go. They clearly weren't more specific so they could leave the 'cake and eat it' option open but it's quite clear to me that what is said there means leaving the SM and CU.
- "We'll be in charge of our own borders" and "We can control immigration". That quite clearly means leaving the SM unless the EU gave us the cake option which couldn't happen given they gave Cameron nothing when he asked. Again it seems strange that the classic trope is leavers are racists and it was all about immigration but that it wasn't a vote to leave the SM.
- Less so this time but still quite clear, when referring to remaining "The European Court will still be in charge of our laws" - this will still be the case if we were to ceteris paribus stay in the SM (though less so with the Swiss and Norwegian model).
- "We'll be free to trade with the whole world" and "The EU stops us signing our own trade deals". Again it clearly means leaving the CU unless the EU gave us a cake option. We can't do any of that in the CU so that means leaving the CU. That is pretty clear.
Maybe you wanted it more to be more explicit, maybe you think people didn't understand what these things meant, but there are clearly references to leaving both the SM and CU there, it's pretty clear to me that was the intention unless there was a cake option to be had.
Finally, I do struggle with this denial that voting to leave the EU doesn't mean leaving the SM and CU. Well more I struggle with the fact people don't seem understand why it means that. It's a valid interpretation to believe that voting to leave the EU was a vote to leave the two vital, key agreements/'institutions' that are essentially the backbone to the functioning of the EU. They are essentially the EU. Again I say this fully in knowledge that is not necessarily favourable to my preferred evolution, but that it's a valid interpretation doesn't mean the government has to act on it.