iserith
Magic Wordsmith
Oofta quoted above the rule from the 5e DMG that says: "You can also compare the DC to detect the trap with each character’s passive Wisdom (Perception) score to determine whether anyone in the party notices the trap in passing." I think that's pretty strong evidence that using passive perception in this manner is appropriate in 5e. (Unless you view doors and traps as different?)
I can't see that poster's posts, but I am very familiar with that section of the DMG.
Secret doors and traps are in my view different, though one could argue they both work as per the rules for finding hidden objects (Basic Rules, page 64): "When your character searches for a hidden object such as a secret door or trap, the DM typically asks you to make a Wisdom (Perception) check." This section also sets forth a requirement of reasonably specificity for finding hidden objects.
The section on traps in the DMG is in my view poorly written and edited as it sits in contradiction to the rules for passive checks. The specific line you quote really works only in the context of Activities While Traveling (Basic Ruls, p. 67-68), which is how I presented how I handle such a thing to @Elfcrusher. This section conflates actions and checks as D&D 4e does. It refers to "active" and "passive" tasks which aren't a thing in D&D 5e but are a thing in D&D 4e. In order for it to work, one has to be running a game like D&D 4e where a passive check represents a character not making "active" use of a skill. Which is fine, if that's what one wants to do. I do not (being a proponent of running each game distinctly, according to their rules) and I don't think it's possible to square up the DMG with what the rules for ability checks and passive checks say outside of something like Activities While Traveling.