why S.H.I.E.L.D. picked the baseball game to play to Rogers

When we see Rogers wake up following his unfrosting he’s looking like but then clarifies he recognizes where he’s heard the game before that’s being played on the radio. My question is why did S.H.I.E.L.D. pick that particular game? My theory is once he was completely out of the ice that encased him and the doctor who said, “oh my god! this guys still alive!” the doctor must’ve realized that eventually Cap would wake up and they needed a plan to make it feel like to Rogers he was still in the 40s and so with little time to move him while he was still asleep and no time to pick something they picked the baseball game.

That one mistake of not realizing their timing of what they felt Rogers would not recognize or would immediately recognize by not picking carefully alerted Rogers something was out of place. It’s not like they could’ve picked a song that came out a month or week before Rogers went missing because being a soldier he wouldn’t have had any downtime to listen to the radio that much because the Howling Commandos and himself were always busy taking care of all things HYDRA related as well possibly training for future missions.