Here's how I understand it, based on numerous searches of the US Patent Office website, and Nintendo's various press releases.
Rareware was a small company owned 100% by the Stamper Brothers.
Then they sold a chunk of their company to Nintendo (and more and more, until it eventually grew to 49%) and started making games for Nintendo, using Nintendo's money. Rare would seem to make whatever they wanted, but Nintendo would always "contract" them to do it.
Then Nintendo decided to give Rare even more leeway. They set up "Rare Inc." Basically a big pile of money, owned 100% by Nintendo. When Rare was exceptionally confident in a game, they could have the "Rare Inc." account publish the game, and keep the profits, leaving them with access to an even bigger pile of money.
Every licence Rareware worked on since Donkey Kong Country (except James Bond and Mickey Mouse) was "owned" (according to the US Patent Office) by either Nintendo or Rare Inc (which was owned 100% by Nintendo).
The Stampers were at a high point on the stock-market roller-coaster, and wanted to cash out completely, but Nintendo didn't want to invest even more money in Rare, so they agreed to get off too, and help sell the company to Microsoft.
Nintendo sold their 49% back to the Stamper Brothers on (a quarter-billion dollars worth of) credit. The Stampers sold the whole thing to Microsoft.
Rare Inc. was dissolved and absorbed back into Nintendo.
There were supposedly some statements from Nintendo when the news finally broke out, about Nintendo still owning games like Banjo and PD.
After the sale, Rareware somehow ended up with the rights to all the GameCube games it was working on at the time (like Kameo and the DKR "Mascot Racer"). And all the licences that people would expect Rare to be interested in (Conker, PD, Banjo). Nintendo appears to own all of the licences that Rare had previously said would only be "one shot" games (Blast Corps, Jet Force Gemini).
Whether a licence was owned by Rare Inc or Nintendo themselves does NOT appear to have been a factor. Games were taken and left behind from both Rare Inc and Nintendo.
It's assumable that Nintendo did own everything, but they had no use for most of it, and were apparently on extremely good personal terms with the Stamper Brothers, and wanted Rareware to succeed, so they sold (or maybe even gave) the Stamper Brothers their choice of licences.
One of the Stampers said that Nintendo was beyond good about the whole thing. And they're Microsoft employees now, so it wasn't any lame publicity BS.