The multiple sections where it says the DM doesn't control the PCs and describes the mechanics and reasons to roll skill checks in the first place.

Having a section describing how to do a contested roll isn't the same thing as saying that is how you handle all player vs player skill checks, and it assumes you know that circumstances should affect the rolls beyond the numbers on your character sheet.

Tbf 5.0 is actually pretty bad about splitting up this information between the PHB and DMG, and assuming players have a better grasp of the whole picture than it should.

For example, in that Contested Roll section, it has this paragraph:

"Both participants in a contest make ability checks appropriate to their efforts. They apply all appropriate bonuses and penalties, but instead of comparing the total to a DC, they compare the totals of their two checks. The participant with the higher check total wins the contest. That character or monster either succeeds at the action or prevents the other one from succeeding."

It assumes you know this has to be used with the sections describing things like environmental and attitude bonuses, and the sections on player agency and cooperative play, or for that matter NPC attitude tiers and how those specifically work with Deception and Persuasion, but it's easy to gloss over that line and think it simply refers to a character stat line.

It also assumes you know that rolling that as contest was an option and not a requirement in the first place.