I'm not sure what you mean by 'two channels" and the term "fully balanced" is rather ambiguous.
(Just to stress, I am not an expert. This is just what my understanding is, which maybe wrong. So I welcome better clarification and a chance to learn.)
The two channels are the left and right channel. And what I'm referring to, and on a very basic level, with "fully balanced" being when the circuit maintains the separation of the positive, negative, and ground (i.e. 'balanced') throughout ALL 3 sections of each channel, the input, amplification, and output. This also requires that the left and right channels can not have a shared or common ground anywhere in the 3 sections.
That said, what a lot of preamps, amps, etc. will do is have a balanced input connection, to an op-amp which converts the signal to a single ended (i.e. common ground) amplification section, then back through an op-amp to a balanced output connection. (again, my simplistic understanding). Thus, while the signal is balanced in and balanced out, it is not "fully balanced" thoughout the circuit.
Which leads to the OP quote from 6moons about the Gato:
This is per 6moons regarding the AMP-150, I assume the "AE" version is identical.
"The input PCB sits near the back plate and sports NEC relays and an analog BB PGA2320 resistor-ladder IC. As a single-ended circuit, the XLR i/o ports are convenience items de/symmetrized by a TL07a chip."
- Jeff