He's talking about industrially produced mouldings. They are veneered after they are profiled. These are not super high end items, but are quite common, just like foam mouldings are now common for house construction. It's more or less the same process as seen in cheap kitchen cabinets where the whole door can be veneered with a foil. This also limits the complexity and detail of the profiles that can be created.
Frames have been laminated for centuries, even small ones. Most commonly each profile element is made of one or two pieces, and if there is veneer then it has a flat back and profiled face. If you have some older furniture you might even see this on mouldings.
As to the OP's question about flatness, there shouldn't be any problem getting a 60" piece of wood to lie flat. It's a question of wood selection, drying, and proper technique in facing the board. There are a lot of hints on this thread already about that.