Follow up to this answer
It seems that the Amidah begins with the words ה שפתי תפתח, and not the word ברוך which begins אבות.
O.C. 111:2 indicates that when the Shat'z repeats the Amidah, he should say ה שפתי תפתח aloud. However Ba'er Hetev says he should say it silently.
It seems that if in fact the Amidah begins with this verse, Shat'z should say it aloud. What is the logic behind Ba'er Hetev's reasoning?