The traditional Bernoulli explanation of lift depends thoroughly upon a wing which, through differing geometry between the upper and lower wing surfaces, causes higher air velocity above and below, leading to a pressure differential, which in turn creates an upward lift force. Yet insect wings are nearly flat, and they seem to be capable of generating some lift to complement their direct application of downward force to the air. I get the strong sense this is one of those cases like static and kinetic friction where the first year university description turns out to be grossly oversimplified, and there's some deeper, more true to form explanation I'm missing.
How do insects achieve lift with flat wings, and what am I missing?