And the meat they did eat was lean game meat. It was high in unsaturated fats - like our modern day oils. Not like a steak. A steak is a product of farming. It’s a new invention, <10,000 years. Prior, humans ate almost exclusively nuts, fruits and foliage.
Yes oils are “refined”, but humans have been eating unsaturated oils predominantly for almost all of our existence. The proliferation of animal fats is very, very new. Really, it’s past 100 years. Before that meat was rare, it was a delicacy, very expensive for people.
Now, high sugar is a different story. But the oil thing is complex, it’s not as a simple as oil bad animal fat good and natural. No, it’s very unnatural.
Meat only became more of a luxury in the agricultural age where we started squeezing more and more people into smaller and smaller regions which meant there was no longer enough to go around. So plebs got the carbs, and royalty got the protein. FWIW you can also see this in the groups that have ancient traditions dating back far into the past, like the various tribal groups in Russia, Mongolian nomads, etc. Meat, and many highly creative ways of preserving it [1], remain the majority of their diet. They probably don't date back to the paleo, but at least far back enough to falsify the claim that animal fats are even remotely novel.
[1] - https://www.rbth.com/russian-kitchen/334150-dish-kill-kopalk...