I think you're exactly right. I might be being a little loose with the terminology here. "Well-formed" may be a better term than "solvable" for what I consider a valid puzzle. Even if a computer program can find the solution to one of these difficult puzzles, it would be a very frustrating experience for a human player in most cases. For small 5x5 sizes you could get away with it, though imagine a larger 25x25 puzzle where you have to make one of these branching decisions (a guess) early on. Some may enjoy this challenge, though from my experience of running a nonogram game for 15 years I can tell you most will not.

I'm a little underwater handling the surge of traffic to my game, though when I get a quiet moment I'll run my solver so I can give some more precise answers. Basically my solver iterates over every row and column, marking cells that must be empty and painting cells that must be filled by going over every possible configuration for that row or column and finding the overlap. It does this in multiple passes and generally the more passes it takes, the more challenging the puzzle is. If it makes a pass and is unable to mark or paint any additional cells, then it considers the puzzle to be invalid if the end state is not solved (all clues are not satisfied).

I do find this discussion really interesting. Maybe I should have reserved "Section 666" for these puzzles with unique solution but require a branching strategy :).