Thanks for the info.
I tried to duplicate what you said. I turned the ignition on and measured the current at over 2.5 amps. I turned off the ignition and opened the driver's door. The radio did turn off but would turn back on if I pressed the radio on/off button. But, if I pushed the radio on/off button it did turn off and, after a while the current did drop down to 50 millamps or less. I left the radio fuse in place and the battery still had 12.53v this morning. I did as you said, and did not open the passenger door.
So, it seems the answer is as you said, but I am not sure if I can trust this problem not to repeat. I will have to hope I do not go out to a dead battery again.
Did you find any way to permanently correct this problem?