If you have a standard 1.6mm thick PCB, and you use a M3 or #4-40 mounting screw, starting from just snug or making a contact but exerting no force, a single quarter turn reduces the PCB thickness by 7.8% and 10%, respectively (pitches being 0.5mm and 1"/40).
Arent those vias just underneath the screwhead? Wouldnt they then become rather useless?
Yes. No, because the epoxy material doesn't
compress, it
deforms. Think of clay, play-doh, or dough, and not foam. Instead of expanding in every direction in the plane of the PCB and potentially causing the damage I described (especially to inner conductive layers up to an inch away, say), most of the expansion happens into the via holes, with the plating material acting a bit like glue, helping avoid delamination there.
The reason it makes the PCB stronger is that it allows larger and more varied dynamic forces to elastically deform the PCB near the mounting hole without propagating the deformation further; keeping the deformation localized there.
Like I said, there is no need to take my word for it: this is easy to test with an unneeded board. If this is something that really interests someone, they could design a multilayer board with comb-like capacitive stress measuring structures and various types of mounting holes placed symmetrically near such structures, and test it. One could manufacture a set of five for just a few dollars at JLCPCB even with six layer boards right now. My claim is simple: with vias within the screw head area, at any given screw torque the PCB stress/deformation is minimized, compared to similar mounting holes without vias, or with solder dots.
The image you showed of small "pads" around the mounting hole is new to me; I've never seen that in real life. But plenty of the via kind. I'm not an EE myself, but my background is in physics (mostly HPC and computational materials physics; not this kind of mechanical stress stuff, but atomic level stuff) and before that, in custom full-stack development.