Also, how exactly does the GPU go from 'giving stupid answers' to 'not functioning anymore'? Is there something in the drivers that checks for computing errors and shuts it down if there's too many? Or is it in the miner software? And how can I disable such a process (even at the cost of getting loads of rejected shares)?
Neither miner nor driver are shutting down the GPU it simply stops responding to commands. The GPU is almost like a self cointained computing environment (think OS for math). The host system gives the GPU a kernel to run, provides inputs, collects output, and periodically provides GPU control instructions. Other than that the GPU operates autonomously.
If the GPU is making errors some of those errors could manifest themselves in just computations (2+2=5) some can manifest themselves in flow control. The first will manifest themselves are HW error. The second can manifest themselves are an unresponsive GPU.
When a GPU crashes it often is still at full load. So it is doing "something" just not anything useful and no longer responding to any command and control signals from the driver. There is nothing you can do to avoid that other than not pushing GPU past their point of stability.
As for why does author of BAMT push new users towards cgminer. He feels phoenix is superior. Some of us disagree but he has marginalized cgminer in favor of phoenix. That likely isn't ever going to change.