
look closely - at the circled area in the pic - the piston (as I am talking about a typical fridge compressor not a scroll pump) is exposed on both sides.. but the pressure acting on the other side of it is not at atmospheric pressure (as if it was in case of a tyre pump or a shock pump) but equal to the inlet pressure...
if inlet pressure is 50 psi then to get 100 psi I need to do the same amount of work as when inlet pressure is atmospheric but I want to get 50 psi at the air output
to make this simpler to understand think how shrader valves work... their crack pressure is AFAIK close to 60 psi.... if you connect a chuck to one and provide air at 61 psi the valve would open...
but would it open if the pressure inside the tyre was 200 psi ?? no... how much more pressure would you need to do exactly the same thing which requires exatly the same amount of work ( that is overcoming the force of the spring inside it)?
well you would have to supply air at higher pressure.. at (200psi + 61 psi) 261 psi... just to do exactly the same job - that is overcome the force of the spring that's equal to 60 psi
now before you think that this proves your theory....

....mind you that the spring force in this example is an equivalent of load put on the motor
ok another example... here potential energy of water is used to represent pressure
there is a bucket with water standing on the ground and you have two ideantical pumps that can pump water 10 meters high... so you put the pump in the first bucket and pump water from it to a bucket that you placed 10 meters higher... now you put another pump in the second bucket in order to pump water 10 meters higher... is there more load put on the motor of the second pump than the first one ? no height difference/pressure differential is the same and there is exactly the same load put on both pumps
I really don't know how to explain it better... but it's simple...
I hope this helped