There may be an issue herein, however, involving the difference between the De Jure and De Facto use of skills in D&D 5e. While some may believe that the former is what matters when discussing the game per the rules, I would argue that the latter in some respects reflects a more accurate sense of the game per common practice.
For example, I noted earlier that Dungeon World (and PbtA) don't really have "action skills" either. Nevertheless, players may attempt to trigger or name their Moves in the fiction as if they were. So while Dungeon World does not have "action skills" de jure, moves can cultivate a quasi-"action skill" status through gameplay.
In the case of 5e D&D, as skills are one of the most player-facing means of mechanically affecting the fiction outside (or sometimes within) of combat, would it really be surprising for them to take on an action-like quality in common practice of play?
No, it absolutely makes sense in a common parlance way. Just like I keep using "moot" in the common, but tecnically incorrect, way.
But, if we are trying to have a conversation about technical correctness, then we need to be technically correct, yes? So what I'm interested in is not whether everybody understands what is meant (however technically incorrect) by, "I'll make an Investigation check", but rather that if by accepting that language we are somehow turning "Investigation checks" into a mechanic with the same specificity of, say, the Hide action or the Shove action.
The argument in question is that a skill is specific enough to override the general case. But, really, the way a skill is used it's just an add-on to an attribute. Right? You don't make a skill roll, you make an attribute roll, and sometimes you add proficiency bonus if you have a skill. So, if the theory that skills are specific exceptions to the general rule is to be true, it means one of two things:
1. Attribute roll are
also meet the definition of specific, which basically means
everything meets the definition of specific. Which means the general rule is always overridden, and isn't actually a general rule.
2. Attribute rolls without a skill proficiency aren't specific, but if you get the skill bonus somehow it suddenly becomes specific enough. ???
I don't really think either of those arguments make sense.