Accies have 2 goals every season in the Premiership. One is to survive and the other is to beat us. The derby has always been more important to them than it is to us. I think most fans, rightly or wrongly, would rather see us beat Hearts for example, than beat Accies in a season.
While it's a cliché that the "form book goes out the window" in derbies, it is certainly true. However, we have poor performances across a season - it's just that we notice the ones against Accies for the obvious reasons.
Over the years, I have seen us win comfortably against them many times. In fact the last away game I attended was the 3 -1 game at the start of the 2019/20 season where we strolled it in the sunshine from start to finish.