I think you are right. The term production hive typically is a hive that is for honey production. But, it could, of course be the production of anything, queens, brood, wax, etc....
It is difficult to not become frustrated when doing everything you feel is right, only to have them decide to do something on their own. If you had your bees in double deeps and they were filling it pretty well, then yes, you probably could have removed the entrance reducer. There should be more than enough bees to protect their investment. But that's not saying that is the reason. Bees are very good at controlling the inside temps, regardless of the entrance, outside temp, etc...
Here is how I look at my situation. I have five hives. At this point, I really only want enough honey for my family and a few friends. If every one of my hives produced really well, that would be way more than I could ever use. That would be a blessing. Having the extra hives allows for some "issues" along the way. If you are just starting out, consider this a great learning opportunity and don't beat yourself up about any thing you might blame yourself for.