Your description that the battery is old, sat for over a year, etc., puts the dealer's statement in question. Unless somebody put an actual load tester on the battery, no one can say it's good. If you let a battery sit in a car for a year, it will be completely flat. If that battery has any age or wear on it previously, it's capacity and CCA will be dramatically reduced due to sulfation from storage at low SoC. I suspect the mechanic used the HDS to read the voltage, saw it was okay and never bothered to cross the shop, grab a load tester and actually load the battery. A voltage check is only part of the picture.
The charge light behavior indicates your 12V charging system is operating above idle.
I assume the drop to 11.5V was at idle. Did you check voltage at 2000rpm when the red light was out?
I am not at all convinced that your 12V is good.
Did you look for a missing fuse?
P1639 Code in 2003 HCH? - GreenHybrid - Hybrid Cars