If the transformer output is floating, like driving a headphone, it is a perfectly balanced line. Since we are talking about the balanced output, how the signal gets there can be as simple as an unbalanced line driving a transformer. In the case of the 307A, the 307a is run SE with the transformer as the plate load. Looking at the 307a it is running with an unbalanced input, and true balanced output. Running two solid-state amps to get a balanced line can never be as accurate because the amps have to be perfectly matched, and each amplifier will still present a reference to the power supply rails, where the transformer output is isolated from grounds, or grounds through the power supply.
My two cents best sound at the Florida meet.