Counterpoint: am American and I read it exactly as intentioned the first time. It didn't even occur to me to read it in the context you did until you mentioned it.
I don't watch network news though.
I don’t watch network news either and had the same reaction as OP reading “two students shoot down”
A better headline could be “Widely Believed Math Conjecture shot down by two students.”
Airplanes get "shot down" but people just get shot (not down.) When a person not in a plane is said to be "shot down", it's always in a figurative sense.