It depends on what one wants to talk about with "swingy" -- how you define the word?
If to you "swingy" means something that simply leads to unequal events you have no control over, which can be game-deciding, then yes Black Market is very swingy.
If to you "swingy" means something that often gives one player a strong early advantage that the other often has insufficient good chances of countering, Black Market is not swingy.
You can have unlucky outcomes with the Black Market that determine some games, we know this. But at the same time it also leads to many more important choices that are in the player's control, not fewer, and so is possibly the best card in all Dominion in terms of rewarding skilled play. That's why people like Stef appreciate it, and don't find the swingy label to be at all useful.