Can hard braking destroy a well maintained automatic transmission?

What would actually break and more importantly how?

I’ve been told by a mechanic today that this is something he has seen before but I cannot figure out what would actually cause the transmission to break. I found a small tidbit on Mister Transmission stating abrupt stops could damage drivetrain components like transmission mounts, but there isn’t any explanation offered as to how that damage could occur so I’m still not sure why the transmission mounts would be damaged.

Would using much grippier tires than stock affect this?