The parent did say "subjectively", but I think there's a case to be made that this is even objectively true:
A pound of food carried inside your stomach is located very close to your body's unloaded center of mass. That same pound of food carried in a backpack is placed further away, creating a torque that your muscles need to work to counteract. So it very well may be the case that carrying the food on your back has a slightly higher energy cost.
It's possible that the additional energy is negligible, or at least low compared to the "subjective" increase in perceived exertion. But I don't think the idea is entirely unfounded.
This has been tested and, no, the location doesn’t make a difference to the necessary power output on a bike. Weight is weight as far as the system is concerned.
Another thing that might come into play is simply holding the backpack on your back. If you put that same weight on a saddle bag or frame bag, your power output won’t need to change but you’re not constantly carrying it physically on your back.
That said, weight isn’t as big a factor until you go uphill, which is why you’re seeing the trend to more aero instead of lighter weight bikes.
What you’re describing, however, is the simple effect of eating food replenishing your energy.