Documents revealed by VGleaks revealed that Tequila Works' Rime was initially pitched to Microsoft as an exclusive under the name "Echoes of Siren". The documentation is fairly detailed and reveals both the "elevator pitch" and the games' design pillars.
Microsoft's Phil Spencer commented on Twitter a direct question on why they passed on Rime with: "Part of job is living with mistakes. Passed on Guitar Hero...I can list many misses regretfully. I try to focus on what we did ship"
Either way, Rime is now a PlayStation 4 exclusive and it's one we're certainly very excited about.