Travel warnings typically urge Americans to completely avoid visiting a country for "non-essential" reasons.
But you've illustrated my point: a travel warning against Greece (due to lax airport security) would have little bearing on beachgoers sitting in Mykonos. Nor would it account for the reality that travelers will spend only 30 minutes in any Greek airport, and the odds of having a problem might actually be quite miniscule.
When I say "excessively cautious", I mean there's a certainly lack of granularity in the warnings, and many people (myself included) think the British Foreign Office is a bit more incisive in its travel assessments (even though they also have an "essential travel" warning for Saudi right now).
Whatever you might think about the effectiveness of a travel warning against Greece, I can assure you the Greek government took it very seriously as did many travel agencies.