Admittedly, it's only implied in the section of the DMG about setting DCs. This is something where performance practice comes into play, looking at the Adventure books that WotC produces as examples. Trained-only Skill checks are a tool Perkins makes frequent use of in these campaigns.
In the DMG section about dealing with dice, I interpret the "middle path"--where sometimes you roll and sometimes you don't, and the DM decides which is which--as implying that any proficiency can be a basis for that decision. I mean, per the book anything can be the basis for that decision, and at least proficiency is something on the character sheets.
If you're doing that as DM, you should probably make it clear to the players, so they don't think their proficiencies aren't mattering.