What's funny is that as a kid, I had a friend who thought the same thing and swore up and down that the second Death Star was the the remnants of the first, despite the opening crawl being pretty clear on the matter.
He also insisted that the bounty hunter, 4-LOM, was pronounced "fore-LOOM", but I've later discovered many people pronounce it similarly. I've always pronounced it "fore-el-oh-em", but that's the topic for another discussion! Lol!
Anyway, the Falcon's turret arrangement is frankly pretty poorly executed or explained. The EU (I think) explained it as two separate gravity wells, as mentioned earlier, but I do wonder what GL & Co. were intending for the audience to think was going on in 1977. Part of me thinks the turret sequence was a hold over from a previous configuration of the Falcon and they just never changed it. As I recall, when the original Falcon's "pirate ship" design was altered and turned into the Tantive IV, the current version of the Falcon we all know and love was originally intended to fly upright, like a giant sunfish, with the cockpit on top. In that orientation the turrets would've been on the left and right, not top and bottom, and would've made a little more sense in regards to what we see in the movie.
Additionally, one thing I've never quite understood is how the turrets are actually attached to the ship, especially given the range of movement we see. In many cases, they are pointed straight up or down during that dogfight sequence but are never externally shown that way, instead always facing forward. I think they were simply attached to poles on the full-sized Falcon but I think that was just a matter of expediency, since they didn't actually need to move.