Leonard Ellis writes:

From ATC's perspective, because
he/she declined both alternatives airports, the "emergency" wasn't really an
"EMERGENCY."

An emergency exists when the pilot declares it; the ATC perspective is
irrelevant from that point.

In any case, while ATC should have granted the PIC what he/she requested ...

A pilot who has declared an emergency doesn't require that anything be
granted--he simply states his intentions. ATC's responsibility is to work
with and around the emergency.

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