Personally, I’m not sure. I have fairly decent recall, but I only ever remember one dream per sleep. If I remember more than that, it’s because I’ve woken up before going back to bed again. So if I woke up and got out of bed four times in a night, it’s quite possible (but very unlikely). I remember quite a lot about my dream each night, but don’t even have a hint of a second dream. And my one dream usually seems so long that I find it hard to believe I could have FOUR of those in one night!
I’ve often wondered in the past - where do you draw the distinction between dreams? How do you know it’s a second dream? Sometimes I have pretty major “scene changes”, but I still know it’s the same dream, because there’s always some element of continuity. There have also been a few times where I’ve read other people’s multiple dreams and thought it sounded like they were all really the one thing divided up into sections.
Some people genuinely do have multiple dreams each night, but I don’t think we should jump to conclusions and say that everybody does, based on the experiences of a few. I’m more inclined to think the situation is different for everybody, and I’d rather trust my own strong instincts on the matter.
If you’re worried about TV affecting your recall, I recommend to try and improve it. It can’t hurt to turn the TV off, anyway, even if it doesn’t really have an effect on how much you remember.