I think "Rolling in the Deep" and "Set Fire to the Rain" are somehow relevant to the Olympics when they emphasize on the word "fire" from those songs lyrics as spirit of Olympics.
Hmmm ... I can even think the whole songs, lyrically are applicable for Olympics symbolism ...
"We could've had it all, rolling in the deep" --> as athlete can win all games as long as he/she got full support
"You had my heart inside of your hand, then you play it to the beat" --> that the supporters giving their hearts to the athletes and let the athletes play their best
"I set fire to the rain, watch it pour as I touch your face" --> that sport supporters shower the athletes with warm spirit of encouragement
"Well it burn while I cry cause I heard it's screaming out your name" --> that the spirit will always be burning and the athlete's names will be cheered for their best achievement
Haha ... I know it's a long shot interpretation ... It's just me desperate to hear those songs in the Olympics ... hehe ...