Yes, that is correct.
The IBM PC came along and was basically an open format where Apple was a closed system. The rest is history...
And the history is that Microsoft, not IBM, reaped the rewards of DOS/Windows' success. Remember that the Mac came out in 1984, when Microsoft was still pretty small and the clones were just beginning to eat IBM's lunch. Apple wasn't looking to become the next Microsoft -- it was looking to avoid becoming the next IBM.
It's also worth noting that IBM didn't intentionally build an open system. Companies beginning with Compaq reverse-engineered the BIOS, and IBM lost lawsuits trying to stop them.
An important point often lost in the Apple/Betamax comparison is that Apple made a conscious decision to keep the system closed, because the whole Macintosh concept was that the hardware and software were designed at the same time by the same company to work together. That has been the concept for more than twenty years, and it's why throughout that time Macs have worked more smoothly and had fewer complications than Windows computers.