The false thing they teach is that air has to go over the longer side faster. Actually, it’s under no obligation to meet back with the same air on the other side, and doesn’t in practice. The real magic bit is the corner on the back, which is not aerodynamic and “forces” air to move parallel to it (eventually, as the starting vortex dissipates).

The pressure difference from different volumetric flow speeds is real, it’s just not that straightforward to produce, because air mostly does whatever it wants. A lot of aerodynamics is still more art than science, and it’s even possible the Navier-Stokes equations it’s based on fail under certain conditions.