Wrong. What became NT was an "advanced projects" branch of OS/2 that Microsoft was developing. It was originally called OS/2 NT. It ended up being very different from mainline OS/2 because Microsoft dropped things like support for 16-bit CPUs very early on, but it's still a fork of OS/2.
The original project to replace Windows's DOS underpinnings was OS/2. The alliance was short-lived, but that doesn't mean it never happened. After the split, Microsoft decided to also call it Windows, leaving the OS/2 trademark to IBM. But trademarks are cheap. Source code lineages are where it's at.