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I'm a little confused. If the player rolls a 23, and I follow your original suggestion and the "special die" comes up a 1 so then I lie to the player, does that also reduce to either 0, 50/50, or 100? Assuming you're going to say it doesn't, how is it different than I secretly determine a DC of 24, they roll 23, and I lie to the player? Either way, the player sees a really good roll, and is given a lie.
The difference is that the player knows the underlying mechanics. If the player gets a really good roll, and sees the DM roll the secret die, he knows exactly what his odds are, which will be something like 75% if a d4 was used. (Well, if he didn't know the original TN then he might be guessing at the exact odds, but he knows it will be 75% or greater.)
Contrast this with the DM attempting to nudge the conclusion toward the correct one without making it obvious. There are no underlying mechanics, so the player has nothing from which to derive predictions.
In my case, the lie is because they misunderstood the situation to begin with, and they were dealing with a master rogue only posing as a guard, and thus the lie is justified. (If there wasn't such a setup, the 23 would have been a runaway success.) In your case, some dice the GM rolled in secret just ripped them off. Is that better? (I would claim, no.)
I think a critical difference between us (and between me and many of the posters in this thread) is that I inherently don't believe a skill roll should determine things that can't be known with certainty. Not just because it's unrealistic but because I think the uncertainty is fun.
So, yes, if you believe that a successful Insight roll should function as a Detect Lie spell, then under my system you should feel ripped off.
In any case, the players always have their own roll to refer to. If it was high or low, they have a pretty good idea of success or failure (but normally not 0 or 100). If their roll in the middle, yeah, it may be more 50/50. But they can accurately gauge their own confidence in their performance! If they roll a 12, they may figure the DC was probably 10-ish, but not feel confident enough to take drastic action on that conclusion. If they roll a 6, even if I tell them the truth they're not going to act on it. Regardless, if they felt the social interaction was insufficiently conclusive, they might look for some other action to either support or refute their conclusion from that social interaction, or look for something besides the social interaction to support or refute their intended plan of action. But that's OK -- the first round of combat didn't resolve it, so you go on to a second.
Referencing the bold part, my question is: what determines what information you give them with a 6? Presumably it was below the secret DC, so does that mean you tell them a lie? When you set the high DC for the master rogue they also got false information, so it's clearly not determined by the absolute value of the roll, nor by the gap between the DC and the roll. So is up to the DM's judgment? If so, that's where I have a problem, because if the player doesn't know the "rules" then they won't be able to judge the probability, and from their point of view it's effectively 50/50.
Now, the secret DC could work if the delta between the roll and the DC determined a probability, and a second secret die were rolled against that probability. But at that point we have a second secret roll anyway, so the secret DC is unnecessary.