Yes indeed some companies get paid for endorsements and some rebrand other lubricants. But all large companies are concerned with their reputation, and blindly putting their name on a bottle of junk is not wise. I worked with and sold to many rebranders in the oil industry and all made an effort to confirm that my products were worthy of carrying their name. Imagine the consequences of an gun manufacturer endorsing a lubricant that caused their gun to rust or wear - customers would blame the quality of the gun before the lubricant. At least an endorsement by a major gun manufacturer with skin in the game is better than unsupported marketing claims from the oil manufacturer.
Lubricants that are designed for a specific purpose are usually better balanced for that purpose. For example, jet engine oil formulations are driven by high temperature stability and low temperature fluidity (operating temperature range from -40°F to >600°F) and yellow metal corrosion protection with very little need to anti-wear in a high speed turbine. Car engine oil formulations, on the other hand, are driven by anti-wear in extreme pressure environments and coping with blow-by fumes and water. A jet engine oil would cause a car engine to fail, and a car engine oil would cause a jet engine to fail. This is the danger in using lubricants designed for a different purpose.
The demands on a gun lubricant are much less severe and it is unlikely any decent oil would cause a failure. While I prefer a lubricant that was designed and intended for firearms over say one formulated for jet engines or cars, I believe most oils would provide sufficient protection from wear in a gun, where loads are low and motion infrequent. The differences are likely more significant in areas like rust & corrosion protection and oxidative stability (deposits and gumming). Odor, materials compatibility, and ease of use are other factors to consider. Motor oils offer plenty of protection against wear, rust and corrosion, but also contain metallic additives that are unnecessary in a gun and in theory could lead to deposits (ash) if the gun is not well maintained. Jet engine oils are ashless and very stable, but are based on light synthetic esters which may eat certain plastics or seals. Hopefully a gun oil formulator and/or a gun manufacturer would take the requirements of a gun into account and optimize for those parameters.
TomNJVA