Shouldn't 'hear' be accepted as well?
That sounds like you won't listen to it on purpose, which 듣다 means. 들리다 is the verb you'd use for your word.
What indicates that it's "I," not someone else that'll listen to the song?
nothing. This really can be anyone. However Duo treats me as a default option in sentences without a proper subject/object. So when you see a sentence without them, just assume that this sentence is in first person