I did read the links, and in your 2nd link at the bottom under "feeding recommendations" it says introducing low amounts slowly is alright. "What is the ideal amount of fat supplementation? Although there is no clear-cut answer to this question, it has been recommended to feed no more than 3.5 ounces (100 grams) of fat (oil) per 220 pounds (100 kg) body weight per day. For a 1,100-pound (500 kg) horse, this equates to a maximum of 17.5 ounces (500 grams) of oil per day. Of course, oil should be gradually introduced into the diet, and this level of feeding would be reached only after a two- or three-week adaptation period. Also, the daily amount is best divided into two or three feedings"
and... So, the answer is that yes, fat is safe to feed if done so within certain parameters. Start adding fat slowly to the diet to avoid digestive upset. Increase vitamin E when increasing fat. Use vegetable sources and not animal sources. Beware of adding too much, even of a good thing.
Not trying to start a debate, just making sure the OP understands feeding oils is not terrible IF
done properly. I fed my 2yr.old about 1/3 cup, twice daily for about 8 months. I used it for her coat, nothing else, so theres no need to go dose heavy.