Paleo is a low-carb diet. By consequence rather than design, and it's certainly not an Atkins/ketosis diet, but the emphasis is on fish, meat and eggs. If you need to consume a standard ratio of carbs:protein:fat on the paleo diet you're going to have an oddball variation of what most people do on paleo and be eating lots and lots of squash, yams, and sweet potatoes.
Some folks can handle dairy just fine and do so. Some can eat white rice or white potatos and suffer no ill effects. Those are not outright banned by the diet.
Of course they aren't "outright banned" but potatoes and rice are exceptions to the guidelines.
What are you eating and calling it "paleo"? Practically every meal I have ends with citrus / berries / apples / bananas / etc. Sometimes for breakfast we'll have some sliced up apples, that's 30 or so grams of carbs right there. Sometimes an afternoon snack is just a banana or a handful of grapes.
At a typical Atkins level of 20 grams carb per day, I'd be screwed by the time I'm done eating two apples for breakfast, and I've still got the rest of the day to go.
I don't think I'm unusual in that I paleo it around maybe 4 parts veg, 4 part fruit, 1 part meat, and maybe 1 part nuts and "other (possibly non-paleo) stuff" on a very long term average. I don't think its physically possible to low carb if you eat about four times as much fruit as meat. Its not so much that I eat huge amounts of fruit, its that I don't eat so much meat. I ate a 24 oz steak once and literally felt sick, don't know if it was the massive fat content or some kind of protein overdose or just too much in the belly. Lots more filet mignon than t-bone, that kind of thing. I tend toward larger fraction of fruit for breakfast (aka two pieces of fruit per breakfast), larger fraction of veg for lunch (aka salad bar almost every day) and larger fraction of meat for dinner and a chunk of fruit before bedtime. Individual days vary, this is just average.
Diets that include grains typically expect people will get over half of their calories from carbohydrates. Atkins is the extreme opposite and is virtually a "no carb" diet as the purpose is to deplete glycogen stores and induce ketosis.
"4 parts fruit vs 1 part meat and 1 part nuts" doesn't say much because fruits can have varying amounts of carbohydrates and meats and nuts can have varying amounts of calorie-dense fat. Also how big is a "part"? Grapes and bananas are relatively high in sugar but most fruits aren't carbohydrate-dense and even then, bananas are a genetically modified domestic cultivar and definitely a product of agriculture. Same with apples.
I'm not sure you realize how aggressive you would have to be to get 1000+ calories per day from fruit and vegetable carbohydrates alone. Almost certainly, the vast majority of people on the paleo diet do not eat 4 bananas and 4 apples, a pound of carrots and 2 pounds of spinach every single day. They eat eggs. They eat almonds. They eat fatty meat. They pour olive oil on their salad. They wind up with notably less than than the 200-250-ish grams of carbohydrates that is typical of other diets.
By consequence, Paleo is low carb if, while following the diet, you don't eat a lot of carbs. What you call an "oddball variation" is what some others might call "what works for them".
Some folks can handle dairy just fine and do so. Some can eat white rice or white potatos and suffer no ill effects. Those are not outright banned by the diet.
Of course they aren't "outright banned" but potatoes and rice are exceptions to the guidelines.