A lot of us use a PID that has a manual control mode that simply allows you to hit a button on the PID to switch to manual mode.
I have not noticed very many of the affordable PID's to have this manual mode, other than the Auber one... and it is hard to tell on the ones on eBay and such, so I assume they do not... even fewer of the 1/32 DIN units have this control from what I have seen, and 1/16 DIN takes up a lot of room for a simple PWM boil power control...
Additionally, stopping a boilover or just adjusting the percent power is really easy for *anyone* nearby with a knob, but can be an exercise in memory and button pressing with a PID...
From the OMRON manual:
press and hold < and > for 3 seconds..
select the 'level' parameter
select level 2 parameters
select hand parameter..
adjust < or >
it may stay in this mode just fine, and you can use the < and > buttons to adjust up and down throughout the boil, but if it is like the one on my espresso machine, it goes back to the main menu after a timeout..