I think what's being seen here, as with the other recent thread, is that if a poster thinks about an action as an ability check or an ability check as an action (not true in either case) then they may think the check is actually doing something in the context of the game world (it isn't). This is often why we see certain groups with players who push or ask to make ability checks. That's their "action" and the result does a thing in the world. Push button, get result.
In truth, an ability check is just a mechanic that the DM uses to resolve an action's outcome, when the DM determines the outcome is uncertain and there's a meaningful consequence for failure. You don't "use skills" or "make a skill check" to do a thing. There are no buttons to push as such. You just attempt to do a thing and the ability check resolves the outcome, when the DM decides an ability check is appropriate.
When this is understood to be the case by the group, then what is outlined by the OP in my experience actually starts happening at the table and questions as to whether a PC can be influenced by a "skill check" the "NPC" makes are easily answered (hint: no).