Here's some more details, culled from notes and postings I've made.
Briefly, the heater wire is coated with an insulator, alumina, having a certain breakdown voltage. If the cathode-to-heater voltage exceeds this breakdown voltage then current flows from the cathode (higher potential) to the (lower potential) heater, degrading the heater's insulation (which flakes off for further degredation) and ruining the tube. That current flow causes the hum. Once the insulation begins to degrade nothing can save the tube. Consider why 7199 tubes are in such short supply. In televisions, for example, the 7199 failed from heater-to-cathode arcs when the insulation failed. Circa 1995 Matt Kamna reported the the 7199 leakage issue as being caused by heater-to-cathode limits, so this was a well-known issue. This explains why the 7199 fails with alarming regularity in audio equipment.
While the tubes often specify 100 VDC, this is unrealistic as it exceeds the insulation's limits. By the time the tube fails it would be hundreds or thousands of hours and the consumable would be expected to fail, even though it could last longer without the abuse.
Leakage occurs in every single tube with elevated heater-to-cathode potential, and the amount and rate depends upon the thickness of the insulation, both in general and in specific instances, such as where the heater was bent. Current flow gradually erodes the insulation until the leakage becomes an arc.
The solution is moving the relative potential of the heater up so it is lower than the cathode-to-heater breakdown voltage point. This is published for the tubes. A number of amplifiers do not properly elevate the heater voltage. A resistor ensures you don't pull too much B+ current into the heater supply. A few mA is all you need, just for stabilized dividing, since it is a potential not a current.
The published limits are about 90 V, but RCA and others published studies showing that any difference above a few volts difference begins to migrate metal. Either nickel from the cathode sleeve into the tungsten filament or tungsten and alumina into the nickel cathode sleeve. This is why the tube specifications list a different value for the positive potential difference vs the negative potential difference; the polarity determines the direction of migration. The higher the voltage the faster the migration. Metal migration is why two different values are specified in the datasheets, depending upon whether the heater is positive or negative.
Elevation moves the range from the normal range of +/- 3.15 VAC (the voltage moves above and below the 0 V baseline) to that same range but with a different baseline. So, if the heaters were elevated to, say, 200 VAC, the range would now be 200 VAC +/- 3.15 VAC. This just changes the baseline from which the voltage fluctuates.
Elevation process.
AC heater: elevation uses the transformer's center tap so the voltage is above/below a baseline. Neither side is elevated. (range is baseline - 3.15 VAC <= VH <= baseline + 3.15 VAC)
DC heater: the elevation could use only one side (range is baseline <= VH <= baseline + 6.3 VDC) or be split as a fluctuation above/below a baseline (range is baseline - 3.15 VDC <= VH <= baseline + 3.15 VDC).
A Warning
In DC it matters if the heater is positive to the cathode or negative to the cathode, because the issue is pulling metal ions from the cathode sleeve into the alumina and filament, or pulling tungsten and alumina ions into the cathode sleeve.
In AC the change in voltage pulls metal one way then the other. This does not balance out because the movement of metal ions varies with polarity.
Regardless of the type (DC or AC), the voltage difference should be as small as possible to minimize metal ion migration.