To be even more pedantic: the original poster's meme says skill checks don't crit, not that nat 20s on skills are a critical success. Most skill checks in PF2e have a critical success tier. Thus jagermo was correct when they said that skill checks do crit in PF2e.
That being said, you are correct about how the whole tiering mechanic works and a nat 20 not always being a critical success. :)
FYI: once you have purchased 40 unlocks you can get the "Toggler" which lets you toggle off any of the weapons/times/items you have unlocked so that they don't drop in a run. It doesn't let you toggle off the starting items, but it lets you narrow the field drastically if you are aiming for a particular build.