I wouldn't take such a channel that seriously. Their role of existence is entertainment primarily, which can be deducted from the montage work/style (just like barnacules). And that's OK, as long as it doesn't set the new standard O0
As for the point proven, it doesn't really proof or disproof much. Too much thermal paste still exists, at the point there is so much paste that it is a thick coat which adds thermal resistance.
How likely/large of an effect? Probably very small considering on how you tighten up a heatsink on that board. The paste just spreads out, and in this case, there is not much that can short out (non-conductive).
As for ESD, my take on is that it's very hard to kill assembled boards. Power rails will likely have ceramic caps that can 'absorb' an ESD event to a few volts residual. I won't say it's best practice or anything, but it likely won't kill the board straight away.
Any enclosed product that's worth it's name should have ESD and (basic) I/O protection for everything that connects outside.
Cannot say the same for sensitive signals nets like high-impedance nodes, MOSFET gates, etc. And probably also for unmounted parts. So to avoid that, it's probably wise to hold a board near the edges