Just tell them the truth- the power company are a bunch of cheapasses and undersize the aerial drop from the powerline transformer to their house, and then when big motors like a heat pump start up, they draw more power than the rest of the house combined for a fraction of a second. So when the big motor on heat pump starts up, the in-rush of current drops the voltage on the line into the house a few volts. It takes surprisingly little voltage drop to make a notible dimming of lights.
You can even point out that a typical 5hp motor has inrush of 168A, even if it only draws 20A while it's running. Shoot, if the pole pig is only 25kVA, that in-rush would completely saturate the transformer and dim *everyone's* lights.
