This may seem like an obvious question, but hear my reasoning. The rules for flat checks are very specific and unambiguous at a first glance.
When the chance something will happen or fail to happen is based purely on chance, you’ll attempt a flat check. A flat check never includes any modifiers, bonuses, or penalties— you just roll a d20 and compare the result on the die to the DC. Only abilities that specifically apply to flat checks can change the checks’ DCs; most such effects affect only certain types of flat checks.
If more than one flat check would ever cause or prevent the same thing, just roll once and use the highest DC. In the rare circumstance that a flat check has a DC of 1 or lower, skip rolling; you automatically succeed. Conversely, if one ever has a DC of 21 or higher, you automatically fail.
So reading that, it makes sense to me that a flat check cannot be modified by rolling a 1 or a 20, given that it would render the bolded sentence invalid.
However, and any experienced player knows where I'm going with this, Recovery checks read as follows:
When you’re dying, at the start of each of your turns, you must attempt a flat check with a DC equal to 10 + your current dying value to see if you get better or worse. This is called a recovery check. The effects of this check are as follows.
Critical Success Your dying value is reduced by 2.
Success Your dying value is reduced by 1.
Failure Your dying value increases by 1.
Critical Failure Your dying value increases by 2.
Using our brains it's easy to see that the lowest possible DC for a flat check, not counting feats that alter it, is 11. Which means that if natural 20s don't influence a flat check, it's impossible to get a critical success on a Recovery check.
Common sense leads me to believe that the intended behavior is that 20s and 1s still matter on flat checks, but it would still warrant a change in the bolded sentence on my first quote.
Another reason this is relevant is because of the new variant crafting rules in Treasure Vault, where a character crafting a lower level item could have to make a Flat Check with a Negative DC. While impossible to fail, if Nat 1s matter, then you might still ruin your crafted item with bad luck.
As already pointed out, it might seem contradictory but it's not. It's simply setting up boundaries to forgo rolling.
If the DC would be 1 (or lower), don't roll, you succeed.
If the DC would be 21 (or higher), don't roll, you fail.
If the DC is 12, roll. On a roll of:
1 - You critically fail because NAT 1
2 - You critically fail because you rolled 10 less than the DC
3-11 - Fail
12 - 19 - Success
20 - Critical success from rolling a Nat 20
Noting that whatever flat check you have may or may not have separate critical success/failure outcomes.
I see two ways of approaching this.
First, if the flat check has such an extreme DC, why are we even having a check in the first place? What exactly are we hoping to gain from this? That seems to be what that rule for flat checks with a DC of 1 or 21 is going towards - it is just using more diplomatic language.
However, if there was some circumstance where there was a flat check with a DC of 1 and it had both a success and critical success entries, and the player wanted to roll it in the hopes of getting the critical success result - I would probably let them.
Thanks to all that contributed. I can also see this interpretation as valid. This would mean that using the new crafting rules in Treasure Vault, a Legendary crafter can craft at double speed any item that is 1 or lower than their own, a master a 3 or lower, and an expert a 5 or lower.