If you are eating grass fed meat there is no need to be discarding fat.If you are eating commercial animals then the skin/fat should be discarded as all the toxins will be here.
Paleo tends to go with lean meats and primal does not

Practical Paleo (my first resource!) encourages dark meat and skins. Unfortunately I can't stand dark meat OR skin, but I definitely don't get rid of the fat from my grass-fed ground beef.

I try to stick to red meat(ruminants) and seafood as much as I can simply because I like it more. But for those concerned, chicken contains a significantly high level of Omega 6, especially in the skin and drippings.