Traciatim is right about modern CPU's being able to play 1080p, but I'd still go with a low end modern card. Large MKV's can be a bear to render.
Honestly your friends budget is a bit high for what you've listed as requirements. It's surprising how little horsepower you need for a killer (non-gaming) HTPC. I can play 20gb 1080p MKVs perfectly with a pentium d + a radeon 5450 at 20-30% cpu load on my guest room HTPC. I suppose there are pricey case options but I think <$750 with be way more than enough.
My suggestion is go with a smallish 120GB SSD, 3-4TB platter, something similar to a 6570 or R7 240, anything above Pentium G3220, BR drive, whatever case he likes, <75$ micro atx MB, win 8.1 (best htpc OS to date). That would make a killer box but honestly you don't really need the SSD. I use them in my HTPCs but when you think about it you're not turning it on and off all that often, and without all the normal stuff one puts on their main PC the boot time will be pretty quick with a decent platter.
Next consideration would be a cable card tuner, but that brings WMC into the equation. The nice thing about the tuner card is obviously a separate DVR, being able to convert TV to formats like .mp4/m4v for viewing on portable devices, also its nice to be able to capture something permanently. My wife has been on TV a few times in the past year, I have enjoyed being able to share the appearances and keep them forever.