Back in 1979-mid '80s, our Mules (USMC) were a mix of older green ones and newer MERDEC ones, mostly Winter Verdant as that seemed to be the almost standard camo for Marine vehicles. In Panama, we did use the Jungle scheme with predominantly green on vehicles, but I don't specifically remember any Mules painted that way.
I don't like being critical of other folks hard work, but museums should research their subject and make sure they get things right, because they are often viewed as a reference source. That Louisiana Mule is very nice, but it does bother me when a museum restores a vehicle in a totally inaccurate scheme.
The only time you would see a Mule painted 24087 with stars with Marine markings was if it was a 'reallocated government asset", which was the polite term for items transferred from the Army (with or without their knowledge).
Cheers