Interesting, I'd forgotten about it... Now I remember being surprised when I first saw that document.
My theory (for all it's worth) is that the Air Corps had already told the various companies that the winner of the new super bomber competition would get the B-15 slot. Martin decided to call it thusly but lost. However, since the Air Corps saw some interest in the Martin project and perhaps needed a "Plan B", they officially designated Martin's "B-15" as the B-16.
Funny that the very same scenario took place some forty years later when the various FX contenders all submitted "F-15" projects (as shown by company documents), though of course only the McDonnell Model 199 won and got designated this time.