Toyota and Waterfall methdology for developing software

As you may know Agile software development is inspired by the principles of Lean Manufacturing which in turn is derived from the Toyota Production System (TPS). One Agile methodology, Lean Software Development even borrows the name Lean to make the connection explicit. Since the principles in Lean and TPS have much in common with how Japanese always have approached manufacturing and that TPS supposedly permeates the whole of Toyota, it comes as a real surprise that Toyota uses a waterfall process for software development!