WMG / The Men Who Stare at Goats

Angela Lansbury did know.

Just not the Angela Lansbury the army contacted.

The goat really did die from a psychic attack.

It's too much of a coincidence for it to drop dead at that exact moment.
http://tvtropes.org/pmwiki/pmwiki.php/WMG/TheMenWhoStareAtGoats