I get what you're saying, but I think some of it isn't accurate:
1) For Microsoft, numbers don't matter to them until they outsell the competition. We know this to be true. We saw this a month or two ago when they outsold the PS4 in the US and in the UK by 1,500 consoles, and they rolled out the trumpets, the choir, and the theremin player to announce their hardware victory. They didn't actually do that, but they made sure their PR person earned their pay. If you believe they don't care about numbers that's ok, but there's not a single known corporation in the world that doesn't care about numbers.
2) They didn't win last gen. The Wii took last gen, and second place -- to date -- is still a guessing game due to the absence of a 'final' tally. Most people agree and or believe that the PS3 overtook the 360, but I don't have any numbers that can verify that to be true. 360 won NA against the PS3: you're not wrong about that. I'd go even further and say that were it not for Sony's late-gen efforts with UC3, Journey, and TLoU, and were it not for Microsoft stumbling with Halo 4, Xbox would have taken the title of best software of last-gen.
3) With the 360, they did put themselves in a great position. They recovered from RROD, knocked it out of the park with XBLA, made Xbox Live the best multiplayer network on consoles, and although it never actually worked as advertised, the Kinect boosted their hardware sales to new heights. Now here's where it all went wrong. What they ended up doing -- by "they" I'm referring to Don Mattrick, Phil Spencer, Yusuf Mehdi, Aaron Greenberg, and others -- is adopting a mentality towards console gamers that they've held towards PC gamers for a long long time. It goes a little something like this:
"F*** you, pay me."
This mentality resulted in a product and a vision for their gaming arm that was so headscratch-worthy that you seriously started to wonder if they were planning an exit from the console business. You seriously questioned if the Keighley interview and the Major Nelson This Is Sh*t tour and the Agent Phil confusion were calculated moves to devalue the Xbox brand as much as possible. It was just so bizarre!
So overall, you're not wrong: they got the brand recognition with the Xbox 360. But with the Xbox One, they killed any whatsoever goodwill and brand recognition they had created with the 360, and this is why we're now seeing MAUs and number of times a cat meowed next to an Xbox blanket as a metric they use to 'announce' hardware figures. It's unbelievable how much those four guys damaged the Xbox brand.