The equally important question, is how do I reprogram my AVR when my user code hangs the chip (shortly after reset)...Nice to have a feature that works no matter what is or is not programmed into it.
As already mentioned, it is either a case of pure logic, or some logic and code in a rom used to implement this feature. Simple enough for pure logic.
Just because a pin is labelled reset does not mean the entire design has to be reset by that logic. Look at JTAG for example (on chips that have it), tends to have its own separate reset from the primary chip reset and is or may be completely separate reset domain from the primary chip reset. Reset is just another input that is used however the designers want, no automatic reason that every bit of logic has to respond to it.
There is obviously logic and perhaps some code that is not in that reset domain (is essentially in the power on reset domain, and/or inverted reset, when you release the reset pin this logic itself may go into reset and when you assert the reset pin this logic may get released).