Hi Jeroen
Many thanks for all the details on this.
I think there are two issues here ? but please correct me if there are more

1) Returning activity to a HAC app after its HOME had been pressed produces a system error message.
Unfortunately I cannot repeat the errant behaviour despite using a debugger and your Test app.
I have tried several devices, G1(Dream), HTC Hero, HiApad and Kindle Fire, plus emulator with 4.1 .
The debugger messages show the HAC app being sent to the background then returning to foreground without any issues.
I wonder if it is something specific to your device.
I'll keep looking into this because its clearly a bug and needs fixing

2) Killing HAC apps using apps like Taskiller.
HAC apps are meant to run continuously even when in the background(perhaps idling). Quitting is meant to be done either via their menu bar Quit option or else programmatically using the Quit command.
One reason why HAC apps cause a system error message when forcibly quit by an external app is that HAC apps have both an Activity and a Service running. So perhaps Taskiller kills the Activity and damages the running Service.
I wonder if any of the non-HAC apps you tried had their own Services running or perhaps they were all just Activities.
Quite a bit to think about here

Malkom