It's not that I think your interpretation is clearly wrong, it isn't. It just that you quoted one sentence, that is summing up 4 paragraphs of buy phase explanation, IMO out of context. The first two of those paragraphs start with
> First you can play any number of Treasure cards from your hand, in any order....
> Then, you can buy one card, costing as much as you have or less....
I think this is a strong indicator for a conceptual division of the buy phase (though not explicit, agreed). Also the sentence you quote says "You cannot go back and play more Treasures..." If you played a Black Market during the Buy phase, there would be no 'going back', as you never left the part where you play Treasures. Again, in the context of a base Dominion rulebook that just two paragraphs before feels necessary to say that "Buying cards does not use up Treasure cards; you still have the cards." it should be a possible interpretation that the sentece you quote refers to the normal buying in the buy phase.
But again, there isn't really a "Treasure-playing part" explicitly in the rules, or even mentioned on any cards. We treat the "start" of phases differently because cards refer to them, and their timing can be noted. This is why a Summoned Transmogrify can be called immediately - it's still the start of your turn. This all progresses very neatly from the basic rules and what's on the cards.
Transmogrify can be called at the start of your turn --> Summon plays a card at the start of your turn --> Summoned Transmogrify goes on your Tavern mat at the start of your turn --> That same Transmogrify can now be called
It's a neat, logical process that you can deduce.
The Buy phase rules come down to "you can play Treasures until you buy a card." No part of these rules says Treasures are played at the start of your Buy phase. In fact, the start of your Buy phase is before "normal" Treasure playing - look at Arena. Dominion players have been playing "I can't play any more Treasures after I buy something" for a decade now.
Now if Black Market were doing literally anything else - playing Actions, gaining without buying, reducing costs, getting resources, trashing, discarding, whatever - of course you could play more Treasures afterward. But Black Market specifically lets you buy a card, which is what matters about Treasure play timing. The official FAQ for Black Market mentions that buying a card in your Action phase doesn't matter with regards to your Buy phase, but the rules are pretty clear about the Buy phase. It doesn't matter whether the Buy is a Buy that uses up one of your Buys (a "normal" Buy) or the special one Black Market lets you do - it's still a Buy.
Let's imagine there's a new type of card - let's call them Preactions. The rules on Preactions is you can play any number of Preactions at the start of your turn. Once you play an Action, you can't "go back and" play more Preactions. But what if there were a Preaction that could play an Action? It would be pretty clear that if that Preaction played an Action, you couldn't play any more Preactions afterward. It doesn't matter that that Preaction playing an Action doesn't count as using up your Action for that Action phase, you played an Action, no more Preactions. That's the rules for Preactions.
I feel I'm just rambling at this point, but really I don't see allowing more Treasure plays after buying a card through Black Market during your Buy phase as being at all justifiable.