Why would someone advise pressing the gas pedal to jump start a vehicle?

If the jump pack has sufficient capacity, start the car as normal.  If it doesn't start, get some jump leads and another car to act as a source, or a bigger jump pack.  Ideally, recharge the battery.

The idea of 'pumping the gas' comes from carburettor days when they had accelerator pumps.   Doing so would introduce extra fuel & make the mixture richer, which would aid starting the car, like using a choke.  

As for holding the gas pedal down, all that will do is tell the ECU that the throttle is in the wide open position, not something you want if you're trying to start the car! 

On carburetor-equipped car - it is a fine art of starting. On warm engine - you need to press on gas just little bit and keep it that way when cranking. On fairly cold engine - do not press on gas at all. On really cold engine - do not press on gas and close the choke all the way or half-way(depending on outside and engine temperature). Pro drivers sometimes don't use choke and start cranking and then start pumping gas pedal slowly (if engine is not catching and not starting yet), then pumping (pressing and letting go) gas faster.

Latter would allow to start from lean mixture to richer and richer one. If you know what you are doing and have big experience - you could catch just right mixture.
If you will overdo it and get to fast pumping but engine won't start - engine could be flooded with gasoline. Remember do not crank starter for too long - you could get it overheated and burn out.

Just added to your wishlist:
My Wishlist
You've just added this product to the cart:
Go to cart page