I have no idea. I agree that the word sounds like "said."
But, seriously, you have to take a relaxed attitude toward song lyrics.
Song lyrics are not good examples of standard English. The lyrics and tune combine to form an impression. Song lyrics may leave out words, distort words, include nonsense words, "bad" grammar, made-up words, personal use of language. They may commit all kinds of language crimes to fit the words to the music. They may choose words just for the sound of the words, whether they are the "right" words or not. They are about emotion, not logic.
And it's often hard to be sure exactly what the words are! On the Internet, "song lyrics" are often somebody writing down what they think they heard, and different sources will have different words.
My personal favorite songwriters are manage to get the sound and the rhythm and the emotion, perfect rhyme and meter, and clear, natural, correct English all at the same time. I'm thinking of Broadway songwriters of the 1920s-1960s: Irving Berlin, Cole Porter, Rodgers & Hammerstein, Stephen Sondheim. But they are the exception, not the rule.