Well, that would be the Current Fastest Path, then, wouldn't it? 
From what I understand, the Shortest Path measures distance and can cross over friendly units. The Current Fastest Path measures turns and cannot cross over friendly units.
Let's take a step back. The intent of the Impossible Path rule is to make sure that a unit doesn't follow the Shortest Path toward its objective to the point where it displays dumb video game logic and butts up against a giant rock for turn after turn. It does this by requiring that a unit which has its Shortest Path to an objective blocked by impassible terrain must instead follow the Shortest Clear Path. The problem is that "Shortest Clear Path" isn't defined in the rulebook. What is a "clear path"?
Let's assume that a clear path is one that is free of movement-reducing terrain and friendly units. Enemy units, from my understanding of the spirit of the rules, should never come into play when deciding what path to follow. The Shortest Clear Path would then be one that reduces the distance between the unit and its objective by the greatest amount without contacting movement-reducing terrain or friendly units. If that's the case, then Shortest Clear Path and Current Fastest Path are, in fact, two different things. It would then be the case that a unit will have one type of alternate route to follow for the Indirect Path Rule and a different type of alternate route for the Impossible Path rule. Specifically, if I'm trying to get around a friendly unit, I would be allowed to go through a swamp if it's the Current Fastest Path. If that friendly unit were a cliff face, though, I'd have to go all the way around that same swamp. That seems... weird.
If the Shortest Clear Path does allow for contacting movement-reducing terrain, then it's now functionally no different than the Current Fastest Path, isn't it? In that case, there's no reason so keep the term "Shortest Clear Path" in the game, which is why I've removed it from my version of the rulebook.