I have seen this argument put forward before, generally refering to the animals inhabiting ice age Europe. Below are the main large mammals inhabiting Europe during the last ice age that our ancestors came in contact with (I hope I havent forgotten any):
Woolly mammoth, Cave lion, Cave bear, Cave hyena, Woolly rhinoceros and Irish elk - these all became extinct by the end of the ice age.
Brown bear, Wolf, Ibex, Chamois, Moose, Reindeer, European bison, Musk ox and Red deer - these all still exist in the wild although many in small numbers now.
Aurochs and Wild horses - these are extinct as species but continue in their domesticated forms as modern cows and horses.
In southwest France there is evidence that Neanderthals and our Cro-Magnon ancestors that replaced them hunted pretty much the same prey species.
The animals – ungulates such as
reindeer, red deer, roe deer, horses
and chamois were the most common prey
– were the mainstay of humans in this
part of the world, according to
Grayson.
There is no doubt that hunting of mammoths, woolly rhino, cave bears and lions did take place, they are due to their size, less common animals. Some may have depended on mammoths but I think that for most ice age Europeans the day-to-day meat came from more common and less lethal prey animals that are still around today, particularly reindeer, aurochs and horses. Animals like reindeer and horses tend to rely on fur for insulation from the cold rather than layers of fat.
As for domestic animals, horses have always been quite lean animals as they need to run to escape predators. Domestic cattle may be smaller than the wild aurochs but I doubt that cattle were bred to be leaner.
It is my opinion that a good idea of the meat and fat composition of the diets of ice age Europeans can be worked out by studying surviving species.