How does a transmission line/Guanella transformer maintain Balun action at high frequencies?
A transmission line kind of behaves like a transformer in some sense: In two parallel wires, if there is current flowing in the first wire, the coupling between the wires will force an equivalent, but anti-parallel current flowing in the second wire. This holds true for any kind of transmission line, even coaxial ones.

Where transmission lines and transformers differ is, that in transmission lines there is a lower cut-off frequency below which the current coupling between the two wires is so low that you can see them as independent wires.

The basic working principle of all these "coax line and ferrite cores" transformers is to extend this lower cut-off frequency by keeping the magnetic fields close and thus couple more into the "other wire" (ie shield) of the coax..