Is there any rumor saying it'd double as a DVR?
It's been hinted at since the Xbox 360, and they recently had a patent approved regarding Console DVR in 2011 (filed back in 2007). The 360 was already a Windows Media Center extender, and Microsoft has shown they're pretty invested in living room media capabilities, so I'd say it's a pretty safe bet. There's also rumors regarding HDMI pass through/Cable TV integration to circumvent set top boxes: http://www.engadget.com/2013/04/10/xbox-rumor-hdmi-passthrough/
Pretty cool stuff if true.