I think it is common to distinguish between whispering something and saying it out loud or aloud. Like if you say something private in a theatre louder than meant, your date might say, “Shh, you said that out loud.” Otherwise “out loud” would have no place at all as “say” alone would cover this meaning.
You’re right about the saying, but I think that explains the malapropism.
So, can you clarify the difference between “to say something” and “to say something out loud”?