OK, depleted batteries and both chargers are behaving as expected. One charger must have a more sensitive "full" indicator.
Technical Support wrote:
With known depleted batteries, does the one charger immediately start to blink green? Or does it start to blink green after some time?
Does the red charger ever switch to green?
A blinking green or solid green charger LED is an indicator of a full charge (or a charge considered complete by the charger). If the charger never goes red on a known depleted battery, then there is a problem.