I have some issues with what's presented in the video. Most importantly, the tube he's messing with has a manufacturing issue (as he mentions). One side flashes very brightly (not the Mullard flash that I'm used to seeing) and the other side doesn't. The other immediate issue is that he speaks in the beginning of "large tubes" having filament failure. I would presume these were something closer to a thoriated tungsten transmitting triode perhaps, which is a lot different than a 12AU7. He then moves to the 5751, but it doesn't have a heater flash...
Next on the solution, so you put a 27 ohm resistor in series with the heaters that you can short with a switch. If you forget to throw that switch, you're either putting only 2V into the filament half (just using his numbers for half a 12AU7). If you leave a Crack like that with the power on, the 12AU7 won't draw the plate voltage down and you will risk damaging the rest of the amp. You could also destroy the cathodes in the 12AU7 in the process because they are not adequately heated.
My last issue is that I have piles of used Mullards that flash, but I can't ever remember throwing one away that had an open heater. This is just anecdotal of course.