So, you're going to ignore pesky things like facts because they don't support your argument? Okay. You've been shown that this is exactly how it was interpreted back then and this is why fudging became a thing in the game. That you don't happen to like it really doesn't matter.
What facts? You seem to be making an assumption and calling it a fact, because there's nothing in the quote, as noted, that says "fudging" and that is the fact.
And, AFAIC, fudging doesn't become non-fudging just because I show you the die rolls. So, you're saying that if I roll in the open and then declare a different result, that suddenly becomes not-fudging? Not really buying it. Player side fudging mechanics are simply an outgrowth of DM side ones. They are exactly the same result. The only difference appears to be one gets your seal of approval.
I violently disagree with the idea that rerolls came from fudging. I mean, rerolls existed in games long before the idea of a single gamemaster directing the game, much less secret die rolls. It's a bit extreme to say that the GM choosing outcomes in spite of what the mechanics used said morphed into using mechanics normally. Your hangup on die roll changes is showing here, and you've yet to do anything to acknowledge the differences pointed out by multiple posters. You just keep asserting that what you want it true, and then telling others that they're doing what you've done (erroneously in many cases -- erroneously in the sense that they haven't done what you've done and erroneously in the sense that you've made erroneous assertions).
Well, I really don't care about getting your seal of approval to be honest. It doesn't affect my game at all. Changing results is changing results. Doesn't matter who does it or how. It's all the same result - the dice are being ignored and someone at the table has their thumb on the scales.
An accidental death and a murder are the same result as well. Please stop making "ends negate the means" arguments.
Do player fudging mechanics work better? I'd say yes. It takes the pressure off the DM for one which means the DM doesn't have to constantly monitor things. It shares responsibility for the dice not taking over the game among everyone at the table. Fantastic. It has the same result of shaving off the rough edges caused by runs of luck (good or bad). Again, fantastic. So, yeah, I am all for player fudging mechanics.
Well, as pointed out, rerolls are not choosing the outcome unilaterally in spite of the mechanics. Which is what fudging is. Fudging is not the same thing, categorically, as a reroll. You keep focusing on results, but that ignores that a reroll may not change the result while fudging always does.
Secrecy or in the open is completely missing the point. That's just preference. Who cares what I or you or someone else likes? It really doesn't matter. We like what we like and we're not going to suddenly convince anyone else to like what we like or don't. But, a better method for achieving the same results? I think we can all get behind that.
No, secrecy aids the GM in choosing the story outcome the GM wants regardless of actual play -- which is what fudging does. Open rerolls are using the mechanics to create the outcome -- no choice by anyone.
Thus, we see player fudging mechanics proliferate throughout the game. In AD&D, you had virtually none. Now? The players fudge dice constantly. Probably every single session if not every single round of every single encounter.
There are no player fudging mechanics in D&D. None. But if we use your weird definition of a reroll being fudging, you need to start with chapter one in AD&D with the various stat generation methods therein.