The Bajan singer was approached by the song's producer Jeff Bhasker, who admits the Umbrella hitmaker was "kind of a muse" for the group.
However, Bhasker believes "wires got crossed" during early negotiations with Rihanna, so they chose a relative unknown, Janelle Monae, to sing on the track instead.
He tells MTV News: "(The band) said, 'Who can we get?' And I said, 'Let's get Rihanna'. We were shooting for the stars on everything and she was kind of a muse. Someone (from the record label) tried to reach out (to Rihanna) and I know she heard the song and liked it. But I think some wires just got crossed.
"But everything works out for a reason and Janelle worked out to be the perfect choice. She brought the right element of a great soulful flavour that we wanted for the album."
The pop-rockers went on to win the Song of the Year prize for the hit at Sunday's Grammy Awards.