I think the X1 will eventually be able to run ALL games based on last gen tech in 1080p/60fps.
It probably could from day one but that may not be the best balance of graphic quality and performance. People may want enhanced visuals, better textures, more detailed polygons, improved lighting, improved visual effects etc.
If you rendered a normal 720p 30fps 360 game at 1080p 60fps with no other enhancements it would be a bit rubbish looking close to the original with a better response as you play.
Would you accept a ps2 game on ps3 that is exactly the same except 720p and 60fps? Most would be disappointed they would expect other improvements.
We have already seen Forza do the 1080p 60fps thing on xbox one on release plus it made a few visual improvements but it still looked last gen in many ways and was a downgrade from the game shown at E3 which had more detailed graphics.