Having been inside the company, and watching what they tried to sell, and knowing Berry Gordy's taste from the beginning, and his goals, I just can't imagine Motown trying to hide the fact that they had "White" production people working for them. From Gordy's entry into the music business, he was trying to make music to sell to as many people as possible across as many music genres as possible. He tried C&W, Garage Band, Surf, Rock-a-Billy, hard Rock, Gospel, Jazz, in addition to Blues, R&B and Soul. He failed at selling much of any of the genres other than R&B and Soul, because his marketing people didn't have the knowledge of those markets, nor the connections to get them distributed and marketed in the right channels for the potential customers in those markets to even be exposed to the recordings. He planned to call his record company "Tammy" Records (but the name was already taken). Clearly, he wanted to make good music in any genre which he could sell records and make a profit. This was aimed at the widest audience possible. I think he would avoid at all costs, the image of being an all Black firm. I don't think he'd have tried to hide the fact that "a White L.A. woman played base on many Motown recordings, any more than he'd used a given Black musician. He didn't want the names of his musicians known by the general public, because he didn't want them to become stars in their own right, and demand high salaries, and with that, also have the courage to leave his employ, knowing they could command big money because of having a well-known name as a recording artist.
People at Motown, including Berry Gordy, would only have a beef with Carole Kaye because she deliberately worded her comments, ambiguously, to make it sound like she played on hit versions of hit songs; and then when people took the bait and assumed that she did, she kept quiet and allowed people to believe that; and later, when the questions were very specific, she probably didn't come clean, but rather, confronted with documentation proving her wrong, told lies, to avoid appearing to have been dishonest, earlier. They would have had no problem having her name known as a Motown session player, among all the other players, IF they wanted names of any session players known.
I beg to differ with your attempted point that Jamerson was a "poster boy" and Babbitt received little fanfare from Motown. During Motown's heyday, NO session musicians were touted, nor received credits on records. Only band leaders, such as Joe Hunter, Maurice King, Choker Campbell and Earl Van Dyke received billing (at the head of their band names) on posters and venue marquees. Jamerson never got feature billing until after Motown moved to L.A. Gordy didn't want ANY of his musicians, "White or Black or Yellow or Red" to be known by the public, lest they demand star's wages or fly the coop.