Mostly correct. During the 1990's, MS was obsessed with potential threats to Windows. When Sony introduced the PlayStation they bleated about how it was like putting a computer in the living room and named their gaming division 'Sony Computer Entertainment' and blah blah. MS took the imaginary threat seriously and basically came up with the Xbox to crush what they thought could be a threat to Windows.
It's important to realize that starting in the 1990's and continuing on until today, everything MS has created has fundamentally been a reactionary product. They see a company come up with something, they decide it could be a threat to them, and they come up with a similar competing product. There is nothing resembling a creative impulse at MS, just a constant paranoia about competition and desire to protect their Windows monopoly.
Macintosh -> Windows
Netscape -> Internet Explorer
Java -> ActiveX
OpenGL -> DirectX
PlayStation -> Xbox
Palm -> Windows Mobile
iPod -> Zune
iPhone -> Windows Phone
Google -> Bing
And so on and so forth. Once you understand the kind of company MS is, then you can understand how they could make something like the Xbone.