Answer

Simply put, a law given to Moses at Sinai is a law that was transmitted to Moses from the mouth of the Almighty and passed down through the oral tradition. So it does have a clear source, and the question is unfounded from the outset. There are rare places where the medieval authorities already note that the expression "a law given to Moses at Sinai" is used only to say that this is a firm and binding law, and not literally a law given to Moses at Sinai.