When you talk of fully solved positions, that doesn't really include openings, does it? There are no opening moves that can guarantee a victory, so there are no solved openings. Truly solved moves are all in the late game, where it becomes possible to evaluate all possible moves and know for sure what is the best course of action.
I also think that even in truly solved positions, there are cases where the known best case is a draw or even defeat, but that assumes perfect play from your opponent. If you suspect your opponent can be lured into making mistakes, sub-optimal moves on your part could lead to a victory where in perfect play the outcome would be defeat or a draw.
To take an extreme case, the various 'check mate in 3 moves' openings do work against some players, though they are very bad moves against remotely decent opponents.
I also think that even in truly solved positions, there are cases where the known best case is a draw or even defeat, but that assumes perfect play from your opponent. If you suspect your opponent can be lured into making mistakes, sub-optimal moves on your part could lead to a victory where in perfect play the outcome would be defeat or a draw.
To take an extreme case, the various 'check mate in 3 moves' openings do work against some players, though they are very bad moves against remotely decent opponents.