Well, 4e PHB1 P178 says "The DM tells you if a skill check is appropriate in a given situation or directs you to make a check ifIn D&D 4e, skill checks are often initiated by the player who ask if they can make one. The rules say this and also encourage the DM to say "yes" to the request (though ultimately the DM still decides if one is called for). Contrast with D&D 5e where that isn't said at all. The player describes, the DM decides if a check is appropriate. Players don't ask to make them. At best they can just ask if a skill or tool proficiency applies to an ability check for which the DM has already called.
circumstances call for one."
That sounds a lot like what 5e is saying. The SC rules do talk about situations where a player declares they are using a skill, and some variations on that, and then recapitulates the above, basically, for the "if the player just tells you what the PC is doing in fictional terms." Either way the GM can go back and decide what skill is actually appropriate (or ability, etc.).
You can also see a version of the 3 step process as described by 4e on DMG1 P20, 1) Describe the Environment, 2) Listen to the Players, 3) Narrate the results of actions (this includes checks being made, though it isn't discussed in those kind of technical terms at this point in the book).
Actually, my interpretation of the 4e version is that step 3 can lead to ENCOUNTERS, not to checks directly. While 4e certainly doesn't SAY that there are only checks in encounters, it is actually somewhat implied that this is at least the primary place where they will be used. In my own game my rule is there are ONLY checks during encounters (but that includes challenges, which can be pretty extended).