One way to look at it is that if IBM considered licensing MS-DOS and CP/M to be equivalent, which is to say either one would serve there purposes. Then I can easily see the Chairman of IBM putting a finger on the scale to swing it toward Ms. Gates son. It's like a two-fer[1], IBM is going to do a deal anyway and they figure either OS would work, and he gets a 'favor' point from a fellow board member who he might someday need their vote on a board decision down the road. Politics at that level is all about the banking of favors and opportunistically cashing them in.
[1] "Two for one" -- two desirable outcomes from a single action.
Ms Gates was not on the board of IBM. She was on the board of United Way.