Can you just please add one of the many you use - and not in the list yet? A couple of words will suffice.
inherited stuff: 1232 (several mfgrs)
"My" stuff: The internal supervisor (NEVER the Intel PCA4 kluge).

ANY runaway program may toggle a pin and thus kick an external super, the two different, consequitive writes a proper internal super requires are extremely unlikely in a runaway situation. DO NOTE: there are some chips with internal supervisors that can be turned off/restarted by changing one bit, such chips should be listed in "joke of the day" magazine.

Re noise immunity: I am not quite sure, whether noise immunity in a supervisor is a required feature, really. Think of it, the micro experiences the same (or similar) amount of supply noise and can be thrown off by it quite easily, couldn't it?

The issue here is that if the super is much more sensitive to noise than the uC you get false resets. Now, on this subject, if you use proper 4 layer board with a proper layout, proper decoupling (ultrashort traces cap-chip) etc there is no noise problem. If, however, you are doing it the amateur way it could play a role.

Erik