I am on the opposite side of the spectrum in that yes a child can be overfed if it starts at the beginning with too much milk and gradually the stomach expands to accept the extra food and then requires more to fill it up and the vicious weight circle begins. There is a reason that there are serving sizes and suggested limits set with the Healthy Eating Food Guide. Yes some days a child is extra hungry but generally they should not be eating more than double a regular serving. Their body needs to relearn what it means to be hungry.
It does sound like the child does a lot of sitting in the high chair and likely is fed his meal and then given additional food while parents eat, then some cheerios while they clean up from supper... crying does not always mean hunger and they may have missed those cues at the beginning.