Ok, I'll go, since I'm an EE with some experience in interference coupling and control.

As a material, ferrites have properties somewhat like iron, in that it tends to concentrate magnetic flux when in its presence, like wrapped around a wire carrying current. The magnetic field in the ferrite has an oscillation, since the cause of your interference was a noise current. This oscillation transfers noise energy into the ferrite and reduces the amount of it broadcast into the rest of the universe.

Many ferrites also are able to convert energy at certain frequencies into heat, like a resistor. This is in part where the low-pass filtering you noted (dc gets throught, high-freq noise does not) originates. This action is the "strength" of the ferrite as you called it, which as an EE I'd call energy dissipation. When the ferrite converts that energy into heat, the noise energy is no longer electrical and is not able to radiate and cause trouble to your ROX.

It's not a Faraday cage. Your wire was carrying a noise current from point A to point B, and was radiating noise. I think you said the wire was not going directly to your ROX, yet the ROX was experiencing interference. Your ferrite stopped the noise component of the current hence stopping the noise from interfering with the Sigma any more.

Well done, though it seems like you just dinked with it until it was all better! Professionals in noise control often depend on "experimental skills," too.

What you did was a technique of filtering out the noise, not shielding the sensitive device (the ROX) or sshielding to contain the noise source. No problem, what works, works. And a low cost filter like a freebie ferrite donut or three is a lot easier to set up than a shield is!

Will one ferrite donut work just as well? who knows? If you want to test with other ferrites to see if you can find one piece that works as well as three of them did, great, but don't lose the "good" ferrites. Mark them or store them in their own little plastic bag.