Unless and until the water system pressure in the lines drops to atmospheric pressure I cannot understand how it is possible for water to enter the lines.

Admittedly I am basing my understanding on my well pump in the house, my Groco pump in the bus and my Shurflo back up pump in the bus. Once my water system is pressurized and whatever air has been burped I cannot understand how air can possibly enter the system unless it has been in the system. But having said that, on our buses specifically, if the water tank is full, water system pressure is zero and a faucet is opened, head pressure from the tank primes the pump and pushes whatever air may be in the pump out and into the system. At that point normal water usage removes the bubble of air.

I have no experience with Headhunter pumps beyond a lot of folks bitching about them and a seemingly large number replacing them.