Vertical has mentioned that quite a few publishers are off-l

[Vertical Inc]

Vertical has mentioned that quite a few publishers are off-limits, but if their authors approached you instead it turns into a different story. Though the thing about that was it could potentially hurt their relationship with their publisher. Why is that?

Quite a few? Not really. The total is 4. 4 out of around 50 manga publishers. 
That last question should not be too complicated. In general, publishers act as agents to their manga artists. And in most cases manga artists do not do work on contract. So it is in the best interest for those artists to keep good relationships with their publishers, as they might find themselves without work.
Now, famous artists may have more sway. Artists like CLAMP can work with anyone and they have. But even mid-level artists can cause a stir if they step outside the lines.
Is that fair… Nope. But we also respect the artists’ decisions to keep their workflow stable, even if that means having to look elsewhere for content.
We have run into two situations where publishers issues have been a problem, when the author has approached us. I remember in one case, the author was very gung-ho and even picked up a publisher in Europe on his own but when he approached us, he was threatened with his series being cancelled and his print-ready were not going to be returned. It’s tough.