RPGMemes

I think you answered your rethorical question yourself: If it is not in the official books, it is not an official rule.

And I would not say that they leave it vague. To quote the PHB: "To make an ability check, roll a d20 and add the relevant ability modifier. As with other d20 rolls, apply bonuses and penalties, and compare the total to the De. If the total equals or exceeds the DC, the ability check is a success [...]. Otherwise, it's a failure, which means the character or monster makes no progress toward the objective[...]." That does not leave much room for interpretation. It plainly say that if the exceed, then they succeed and if they don't, than they fail. Yes they don't make an explicit remark about critical results, but they don't need to, because such a rule was never meant to exist in 5e aside attack rolls and death saves.

Not to say that you can't make it a rule at your table (same as with everything else), but there is still not much room for missunderstanding the official print.