It does run counter to what you've said, if it's running locally on the hardware then it's not running on the cloud. You're contrarian, but you're not stupid and I fully expect you understand that "The Cloud" is just a fancy buzzword for "servers in a data centre". Running on the hardware, and running on a cloud platform are two different things, hundreds of miles apart from each other.
Errr..
Unless you're meaning as in talking about a software solution to process the GPU output into recorded footage, in which case I haven't talked about anything like that because as I assumed I'd made clear in both my first post, and later in the visual imagery, I'm of the opinion it's a hardware based solution either as a co-processor to the GPU or built directly into the GPU (well APU) itself. No clouds involved. Seriously, I mock the idea of "cloud computing" and it's supposed usefulness to the Xbox One, so no we're not agreeing on a basic level at all or you think I'm saying something very different. I've also mocked the "always online" component of the Xbone too, and lo and behold that all got reversed (Which served only to make thier cloud computing shtick even stupider).
As for the last bit. Goh is also agreeing on the stance of Cloud computing being bollocks, and "uploading while recording", would be "streaming", aka Twitch, which we'd covered very very early on in all this as being within MS's existing habit of charging for access to others services, but still wouldn't cover the fact the actual act of recording the footage is done on the console, no clouds, no twitch, no internet required, except only by MS's say so in restricting functionality of the hardware you have purchased and own fully.