"They" say a lot of things. I tried bear oil and found it to work fine. May things "work fine". I would not make special efforts to obtain it.
Ned Roberts in his book, "The muzzle loading Caplock Rifle" waxed on about it. That book was a foundational document for the modern muzzle loading resurgence. He may be partly responsible for the legendary status of bear oil.
At the range something with mostly water is excellent. I use moose milk or soapy water. I saturate the patches in a little tupperware and wring out he excess. Spit is popular. I tend to keep my hand out of my mouth when handling lead. For hunting something oily is called for. Lots of oils are fine. Olive oil, neetsfoot oil, mink oil, and others are suggested. The modern equivalent to whale oil is Jojoba oil, whale oil was the holy grail. I have been meaning to try drug store mineral oil (Balistol is mostly mineral oil).
One needs to keep in mind that when MLs were in common use they had no access to petroleum. The kept their guns loaded. That meant using some kind of animal fat. They used what they could get. Bear, deer, hog, and beef were all commonly used.
Try not to over think patch lubes. It really does not matter much. What can matter is using a lube that is to slick, that hurts accuracy.