The thought sequence behind this idea is very simple: We used to roll less or equal in ADED for attributes tests. So, let's do the same with DW. But, since DW uses a 3 branched result tree, let's add the 1/2 success margin.
It's flawed, it's not balanced and it doesn't work well with DW, but it works fine with WD (world of dungeons), although flawed too. Since we play most of WD, with more improvisation than pre-set movesets, we used these rules for the fun of it. The mindset behind those rules are just 'simplicity' and 'fun'. I'm not saying that those lack in DW; on the contrary, I imagine both are inherent of it. I'm just elucidating the thought process that went into the 'making' of those rules. As you see, it was made at the heat of the moment where me and my players though: "Hey, you know what would be cool?".
And you can imagine that other ideas besides that one arose. There are other options, really, for a more 'balanced' way. If you want to emulate the 2d6 with 1d20, you can do as follows:
1-8 = Failure (40%)
9-17 = Tie (45%)
18+ = Success (15%)
In 2d6, the chances for F, T and S are, respectively, with a modifier of 0, 41,6%, 41,7% and 16,7%.
Every +1 bonus in the old 2d6, you can count as +2 in the 1d20. It's not a pixel perfect conversion, for the 1d20 is a linear progression, while 2d6 is not. But it works and it can be used as a more 'betterer' conversion of the DW rulesets.
You may even call those rules 'ADED 1d20', for the first, and 'd20 1d20', for the latter, even though they are not like those rules anyway. Maybe you can call it 1d20- de ADED and 1d20+ the d20, I don't know, lol.
Ps: I remembered other design choice behind the 'ADED 1d20'. Using the rule of rolling under the attribute requires almost none calculation, just matching the number with the attribute. I remember one of the players telling something about that and I riposting 'ok, so we can make like that'. It was cool at the moment.