Any solid dielectric has a finite life, this depends on aging, voltage stress etc. and it's only a matter of time. By keeping voltage stress at a low percentage of its breakdown voltage the MTBF can be extended to the point that it doesn't cause failure at anything like the expected life of the component or product that it is installed in. Class Y caps are a good example of this.
The ADuM4160 USB isolator datasheet has a nice concise summary of this in the Insulation Lifetime section (page 12 and Table 8 )...
https://www.analog.com/media/en/technical-documentation/data-sheets/adum4160.pdfOn that PCB revision of the 34401A, you have a an uncharacteristic HP major cock-up. The GDT is in contact with the metal case of K101, separated only by a poorly controlled layer of paint, which might even have pinholes. If it is never exposed to more than, say, 20V the MTBF of that paint insulation layer could well be so long that it is never noticed (just think how many 34401As there are out there that will never see a problem). Start exposing it to hundreds of volts and that MTBF of the paint layer will plummet.
Yes, things like vibration, pressure of the GDT against to paint
will affect things (although the flow soldering process would have limited this) may affect things, but ultimately it is just a matter of voltage dependent time. The important thing is to make sure that the breakdown voltage of any added insulation fix is a decent multiple of the measurement voltage it will see.