So you know how Stables is good? Those Stables decks you build? Stables is "especially good" when you can't or don't want to get rid of all of your Copper, since in this case it mitigates the downside of having that Copper in your deck. Stables is a lab with a condition, yeah, but then the upside is that it sifts you past those Coppers to provide you extra reliability, and the condition where you need a treasure in hand to make it work is not a huge deal because you have all of these Coppers laying around.
The important part is bolded. Stables doesn't make having Copper in your deck better, it just makes it less bad. Duke makes having Copper in your deck better, but if I'm focused on drawing cards (probably not playing a slog or any other strategy where Copper is actually good) then my choice between Cache and Gold is usually easy (obvs there are exceptions where the only thing I care about is adding extra payload and I'm overdrawing the crap out of my deck, but this is the exception -- Gold is better).
So Storyteller is similar in this case, in fact it's very similar. It's non-terminal draw with a condition, and it has the same Copper-sifting effect. So in this same vein, you don't want to add Copper to your deck unless you absolutely have to, it just helps you draw past Coppers.
But there are differences, too. Most importantly, Stables-as-a-Lab (this means Stables where you actually have Treasures to discard) is a good card in pretty much every deck ever. Maybe not worth picking up at $5 but it's a really good card and it will help you out. Storyteller functions best in decks with high-value treasures, the kind that have been discussed here at length; remember Storyteller isn't worth it if you're only feeding it Coppers, you need to be increasing your hand size with it or else it probably isn't worth it (again, there are exceptions to this but mansies, they're totes not worth mentioning). Like, I think the takeaway from this is that if I want Storyteller in a deck, I may prioritize Copper trashing slightly less, but I would still probably pick it up if it was there, and I certainly wouldn't add Coppers to the deck if I didn't absolutely have to. Remember that exception with Stables, where I just wanted to add payload and I was overdrawing? That totally doesn't apply with Storyteller.
So yeah, the words "mitigates the downside" of Copper I think are appropriate. "Synergy" just isn't accurate.