Well before some kind of mini flame war breaks out between people who like Nintendo and people who don't, i'll try to get in my opinion on this rumor.
The full buyout of Nintendo should be impossible. The company is doing relatively well and it has a very promising product line (Wii and DS Lite). I understand that people believe that the possibility of the buyout is real if you look at the styling of the companies, but still the math doesn't work out.
Now consider this, even though the Wii doesn't have the high resolutions of the PS3, or possibly the power of even the XBox 360, it has two things going for it's self.
1. It's price. I understand that it hasn't been released yet or even had the price presented to the public, but it's reasonable to suspect a price of around 200-250 dollars.
2. A large franchise of games. Along with the usual next generation games, you can also download online various editions of NES, SNES, N64 games, you can play GameCube games, and also Sega announced that it will make it's own library of games (genesis and master system I think) available for download for the Wii.
Apple has experiance with online distribution of music and videos, and there are alot of people asking when Apple will make movie downloads available in the future. The problem is, that while the iPod's screen is good to view if you're on the road, but it's not ideal to view a 2 hour video comfortably. I know you can hook the iPod up to the TV with the new docks, but still.
Microsoft is pushing it's Media center approach by integrating it into it's new OS, and the XBox 360 in a way is replacing the Media Center PC by letting users view photos, videos and music on the TV from your own computer. It's a strong arguement that Microsoft is giving for people (considering the first media center pc's price).
Apple has something similar to the Media Center interface in most of it's current Macs, it's nice to use and easy on the number of buttons needed. The problem is, you need the computer to be physically attached to the TV for you to use it that way, while OK for Mac Mini's, other computers have their own screen's and it's a bit useless at that point. Apple has a good product called the "Airport Express" that let's you transmit audio to external speakers via a WiFi or ethernet connection. Apple could do something similar to produce a video version of this Airport Express. But then, video transmission, decoding, updatable Front Row like OSD, wifi and ethernet connectibility. It's alot, but not completely out of Apple's capabilities. But what do you get with that? Just something more complex than the normal Airport Express.
That's where the Wii comes in, in my opinion. Apple could develop a front row like interface that could be used for various multimedia functions. Like reading video and audio from an iTunes equipped PC or Mac. Along with the built in DVD player, the Wii could be an ideal substitute to an Apple product that maybe not everyone would buy.
So basically, I'd say that it would be more of a collaboration between Apple and Nintendo to bring some more advanced multimedia functionality to the Wii, to increase it's competitiveness with the XBox 360 and the PS3. Also hopefully creating a type of secondary halo effect that will move Mac sales with people hoping to have a more complete or trust worthy (usual problems people can have with PCs) experiance with the Wii and their computers.