iserith
Magic Wordsmith
It sounds like you think this is an important distinction, and that there's a right way and a wrong way to approach skill checks.
It isn't, and there isn't. No need to navel-gaze about the fine points of roleplaying protocol. It doesn't answer the question of "What's up with Investigate and Perception?", anyway.
I disagree - while I make no judgment as to whether there is a right or wrong to it, it does appear based on the responses that how one views the overlap between the two can be influenced by who gets to call for a check at a given table.