Troubleshoot and eliminate the most unlikely, bearing in mind that the more assumptions you have to make, the less likely it is the root cause (Occam's razor).
- the pump does not run during filling, so scratch that
- the only "active" component during filling, normally, is electrically controlled fill valve.
- a high-pitched squeal or whistle is very commonly associated with rushing water through pipes or valves where vibration is the culprit.
I would do these things while the squeal was occuring:
1st- place my hand on the water supply valve and feel for localized vibration; I would also partially open and close it and perhaps close it all the way and reopen it, listening and feeling for any change (this will not hurt the dishwasher).
2nd- I would place my hand on the water supply tubing/hose and move along it as far as possible, again feeling for vibration; I would also attempt to move the line this way and that, listening and feeling for any change.
3rd- I would pull the lower panel and find the electric fill valve. I would again feel for localized vibration; I would also manipulate the supply line at that valve, and tap on that valve, listening and feeling for any change.