I wouldn't invert the d20 test. Part of the fun of rolling, is the instant gratification of rolling high which you've now taken away.
The players rolling but not seeing their roll is probably the best solution to this problem. However if with these knowledge/insight type checks you want to occasionally provide misinformation then I would maybe do something like success is 2 truths and 0 lies, failure is 1 truth and 1 lie. So even though the player knows they likely failed the check, they still have to debate which is the truth and which is the lie. You can even add a secret DM roll that makes occasionally makes failure 0 truths and 2 lies.
The players rolling but not seeing their roll is probably the best solution to this problem. However if with these knowledge/insight type checks you want to occasionally provide misinformation then I would maybe do something like success is 2 truths and 0 lies, failure is 1 truth and 1 lie. So even though the player knows they likely failed the check, they still have to debate which is the truth and which is the lie. You can even add a secret DM roll that makes occasionally makes failure 0 truths and 2 lies.


