Ballmer was only wrong about which Apple alternative ended up capturing a majority of the market.
It doesn't matter a lot to Apple as they have captured a large portion of the segment of the market that is willing and able to spend more, but Android has more of the total market.
Ballmer was right. He underestimated the amount of money they would make, and also underestimated the size of the various markets, and ALSO got it wrong about who would be the "other" OS but......his core point was correct.
They were both right at the time. It wasn't until a few years later that the iPhone was actually competitive. It was really Android (and apps) that changed mobile. None of the companies with great OS teams (Nokia, Blackberry, Palm, Ericsson etc.) could compete with free. All the companies that are successful today are close to the hardware supply chain.
Android only had that opportunity because Apple changed the basic design of smartphones. Until the iPhone, Android was more like the Blackberry of the time. Of course, it wasn't until a few years later that Android phones were decent as the initial ones had issues.
It doesn't matter a lot to Apple as they have captured a large portion of the segment of the market that is willing and able to spend more, but Android has more of the total market.