Yes, I understand that the ammonia is the food - why else would you pour ammonia into your tank in the other fishless method. What I was referring to is that one bacteria 'eat' ammonia and produce nitrite, and nitrite is the 'food' for the bacteria that turn that into nitrate. But something has to break down to create the ammonia.
What I am getting at is that you have to supply a constant level / supply of ammonia to sustain the bacteria through the entire cycling process. Fish provide this in an established tank. If you take out the fish, your bacteria will starve. If you let the ammonia in the tank rise to a detectable level, then remove the source that creates the ammonia, then you choke off your bacteria colony before it gets a strong, solid foothold. After all, to complete your cycle, you will go through a time period where you could add ammonia to raise the level to 1ppm and it would all be gone in 12 hours - but your Nitrite would still be spiking. You need to supply a constant supply of ammonia until ammonia and nitrite are both zero, not until ammonia appears.
At least, that is what makes sense to me. I've never done the shrimp method, so if I'm dead wrong, someone enlighten me.
