Welcome to the site Yorky. Yes, full fat everything is allowed although that doesnt apply to fat on meats and chicken etc. As you mentioned, in moderation. If you are following low carb you will find you dont have the need to be slathering the butter around. Plain Greek yoghurts are the recommended not the fruit types and deffo not low fat as they are full of sugars in the form of rice flour or other sneaky things. My cholesterol was around 7.2 when I started this diet for my diabetes and I have got it down to around 3.5 but I do take a statin daily. But the point is it never went down before even with statins.
I think the science is that your body recognises natural fats like milk, cream, yoghurt and butter and knows how to deal with it. It doesnt recognise chemically enhanced low fat, low calorie etc so stores it away to sort out at a later date, usually in the liver.
Hope that helps.