Paul__B: It is the (AC) electric field. That is why the explanation given is so badly wrong as it refers to the magnetic field which is extremely weak as it essentially only exists between the wires themselves.
What you describe there is exactly how the tubes operate in their normal configuration; in this case the actual current - and so the brightness - is very small (and painless) but the voltage is so high that the gas can be ionised without the cathodes hot.
Thanks for mentioning all that Paul. Definitely nice that you and Mark mentioned those things. Not great when the wrong info gets passed along like that (on that website).