I found a source, the Kaf HaChaim 64 who says:
סד) שם, בשעה שהצבור מתפללין, פי' דווקא לכוין בשעה שמתפללין תפלת י"ח
אבל לא שאר התפלה
At the time when the community daven, that is specially to intend for
the time they are davenning the Shemoneh Esrai but not the rest of the
Rav Asher Weiss shlita answers the scenario of synchronising a private minyan with the time of one's normal shul minyanim in his list of Corona-based sheilos and teshuvos here p.88
He seems to suggest that it is a reference to davening in general and not amida in isolation. He mentions that is worthwhile to have a collective set time for davening so that we ...
Trump's logic that local communities come first is in line with Tractate Nedarim 80b:
מעיין של בני העיר חייהן וחיי אחרים חייהן קודמין לחיי אחרים
A spring in one town should be used for the local citizens drinking as their lives come before the lives of citizens of the other Towns.
Israel did exactly the same with its ventilators refusing to provide ...