I’m tempted to wonder if there might have been some influence on the phrase from the lyrics of “Secret Love”, in the musical Calamity Jane, which was a number one hit for Doris Day in 1954:
“Now I shout it from the highest hill;
I’ve even told the golden daffodil.
At last my heart’s an open door
And my secret love’s no secret any more.”
OK, it was a hill Doris was on, not the rooftops, but she WAS shouting ...