HF signal in a null experiment. What is the exact mechanism?
The question is: by what exact mechanism is a signal generated by the grid dip in the probe?


See the image below:



Any changing magnetic field passing through the red shaded area induces  voltage measured by the probe.

The voltage is given by Faraday's Law of induction:

\$v = \int_A \frac{\partial B}{\partial t}da\$

EDIT1:

To answer your question where the changing magnetic field comes from:
The single wire acts as an antenna (e.g. by its capacitance against "infinity"). I.e. there is RF current going through the wire causing an RF magnetic field. That field is picked up by the loop.

EDIT2:
To answer your question why the is only a signal if you touch the probe with the wire:
The wire alone makes a very ineffective antenna for your RF of 5MHz (wavelength is several 10s of meters), so there is not much power radiated. This changes dramatically if you connect it to the grounded probe.
See image; blue color indicates the current path and strength:


Note also that making the loop smaller doesn't help a lot to minimize the signal because the magnetic field is generated mostly by the current going through one side of the loop. So most of the magnetic field will always pass through the loop area no matter how small you try to make it.

BTW: generally if you have a RF voltage signal at shorted probe terminals I think it will be very difficult to find any other explanation than induction by a RF magnetic field passing through the loop formed by the terminal wires.