Maybe it's just me, but if I need to be at a meeting I would never schedule a flight with an arrival time so close to the meeting time. Sometimes you gotta bite the bullet and fly "the other airline" if it's a more attractive schedule. Or schedule the meeting later.
I agree. Although it's annoying when airlines don't get you to your destination on time, for an important business meeting it's crazy not to anticipate that your flight might not be at least an hour late. In a situation where your whole trip is dependent on this one meeting, flying in the night before is probably the right solution.