Well, it got more interesting. The Toyota dealership finally acknowledged that the Rav4 has the ECU/Gearbox problem that affects part of the 4.2 series.
On Wednesday, they rang to explain the problem to me (Ha!) and to say that they were waiting to see if Toyota would pay for the repair!
To my amazement, they rand again on Thursday to say that Toyota had agreed to replace the ECU and gearbox, but that it would take a few days. I'm really quite astounded and my confidence in Toyota is restored.