Microsoft have said it as well.
They have also partnered with AMD and OEM vendors to put that "Magnus" APU(or maybe it's a different APU line entirely, unsure) and it's variants in any Windows device that will have it going forward. I think this is where this confusion stems from. People are conflating Microsoft's moves with the Xbox app and the OEM devices and their actual home console.
Microsoft cannot legally just "allow" Xbox games, (as in previously purchased Xbox/360/XBO for explicit use on Xbox consoles) to run on Windows pc's. They have to have that piece of hardware. It also, quite importantly, removes the need for any additional emulation/translation layers, so the games themselves should be quite performant, but that strays from the point.
There is no next gen Xbox singular, it will be the Microsoft produced home console, and then OEM... home consoles, gaming pc's, laptops, handhelds, etc. This is achieved via the XBOX x AMD partnership.
I think the big, ACTUAL question is whether or not you will be able to access your pc game library from the home console.
Considering there are no obvious binding legal ramifications there unlike with the inverse (Xbox console games running "natively" on pc) and there being LOTS of rumors regarding this supposed feature, I'd say it (the next gen Xbox home console) will give you access to your PC library, simply because it would be such a banger selling point, and quite frankly Xbox needs those more than anything.