I've seen plenty of transformers physically constructed with both (or all, if more than two) windings wound concentrically around the center of an E-core--in fact, that seems to be the most common type of transformer out there. And yet, the only thing separating the primary from the secondary in this case is a thin layer of plastic--I've even seen some in which the inter-winding plastic was actually torn through in places (presumably because it was wound too tightly). And these transformers are ubiquitous in chargers and cheap power supplies, where the primary would be 120/240V mains!
So my question is, how on earth can you have good isolation between the windings in this situation? Magnet wire is certainly not sufficiently well-insulated on its own, and I can't see how that super-thin plastic between the windings could possibly make it isolated enough to pass safety checks.
Or do they not pass safety checks, and that's why they're so cheap?