The closest the Milwaukee Road came to a classic "Athearn style" caboose (an AT&SF prototype) was its steel drover's cabooses. Those were in fact the first steel cabooses on the Milwaukee Road. They had the offset cupola of the Athearn type caboose, so the general outline is not all that far off, but the window arrangement on the sides differed, and the windows were large, almost like a passenger car (because in a sense that is what they were). Originally painted boxcar red, in the late 1930s they were painted silver/aluminum with black lettering, numbers and grab irons. There was a large C. M. St. P.& P. herald on both sides below the cupola.
Alas the silvery aluminum faded to gray so at some point they were repainted orange. And once stock movements ceased on the Milwaukee Road the cars were released to general service -- I photographed one (painted orange) on the back end of a train heading west out of Milwaukee in the late 1970s/early 1980s.
When they were painted silvery aluminum they were virtually exclusively seen on the west coast which is perhaps where Irv Athearn saw them.
So to answer your question, the paint scheme is kind of authentic -- perhaps more than the plastic car shell itself -- but only for a fairly brief period of time.
My source for this information is Milwaukee Road's Steel Cabooses by Jeff Kehoe, a soft cover book published by the Milwaukee Road Historical Society. If information of this kind is important to you, I strongly recommend joining the Society.
Walthers has offered authentic HO Milwaukee Road bay window cabooses in a variety of paint schemes. They have also been released in brass. Fox Valley Models has authentic Milwaukee Road bay window cabooses in N scale. At one time they also had authentic transfer cabooses that some hobby shops might still have.