Personally, I think it really surprises people how much "real food" they can eat once they get the sugary sauces, chips, and sodas off the menu. The empty and non filling calories add up quick. This may lead to the mis understanding that you can "eat all you want" as long as its good. More like "you won't feel like over eating" if you stick to the "good foods", is closer to reality
I think that about hits the nail on the head. I'm almost certain you can over eat from just natural protein and fat sources, particularly if you make a concentrated effort to get loads of fat in there. However, it's not easy, I doubt that most could over eat it even if you asked them to which, as you said, leads to the idea that if you cut carbs, you can eat however much you want.
I seen this picture on facebook recently which i can't be bothered searching for, it had a plate of about 8 different fruits next to a Snickers, showing that they're equal in calories, saying something like, "you think you will still be hungry if you eat healthy?". I think that's a good example since it's carbs vs carbs in that case. There's a significant difference in how you feel after eating 8 pieces of fruit vs 1 snickers, and potentially a rushed trip to the nearest bathroom shortly after all that fruit, but atleast they actually have some nutrients in them.
Eat "nutritious unprocessed food". Why count calories if you don't need to? If you need to then, yeh, go ahead and count. This is normally for people who are already dialled in as it is but "normal" people struggle enough with change as it is. It's unlikely but yes, still possible that you'll over eat with even "real" food but it would take a real concentrated effort to do so.
Also, as an aside, I have 2 interesting clients just now. Both do over 12 hours of exercise per week. One, I reckon, eats about 1000 calories per day, if i'm being generous from her food log. The other i've worked with little longer so she eats more now, but she was under that amount, and she actually trained to up to 16 hours per week. She essentially ate less than me yet exercises 3 times as much me, but i'm leaner. I have a few examples now where i've increased food intake and reduced exercise volume and it's lead to fat loss - all in women, too, which may or may not be relevant.
I've mentioned this to people before and they just say, "they lie about what they eat" but, I don't think so.
Most people just need to eat "better", I think. "Better" is relevant to the person.