I did some searching online whilst waiting for the Tow Truck, and found that someone had a similar problem that was related to the IBS (internal battery sensor) on the car, but I'm not sure if my car utilizes such a sensor.
This is probably the issue from what you have started. The battery has a charge but nothing happened except the alarm until that stopped.
How old is the battery? If it's original then expect problems but this is different because it has a charge.
I am NOT an expert, but it may be the IBS as you have already searched.
Keep us updated. This is a unique scenario and it may be helpful in the future to other people with this problem.