As a rule, BattleTech rules are pretty literal and trying to extrapolate or read between the lines will only lead to needless headache.
The PSR for 20+ damage is really one for taking 20+ damage in one phase -- says so right on the table on Total Warfare p. 60. Since the Weapon Attack and Physical Attack phases are distinct, damage from the one doesn't carry over to the other for this purpose (any more than you'd worry about damage taken in the previous turn, for example).
Likewise, the PSR for being kicked is specifically for being successfully hit by a "kick" physical attack; it's in fact part of the rules for making one (TW pp. 147/8) and explicitly applies regardless of which location ended up taking the damage. So, taking a punch on the Kick Location Table is still a punch and doesn't force a PSR because punches in and of themselves don't do that (though the damage inflicted by said punch to the leg still might just like any other hit), while being kicked on the Punch Location Table is still a kick and requires the PSR to avoid falling over as normal.