Reading on this a bit more, it looks like I was off on B12 specifically. Vegetarians can get this from eggs and milk, but full vegans need to either eat plant-based foods that are fortified with B12, or directly take a B12 supplement.

So my first sentence should actually be, "All essential nutrients humans need can be provided by a plant-based diet." That is accurate because it includes fortified plant-based foods, plant-based direct suppliments, and vegetarians.