This is my standard spiel when I hear the words "acid wash." Where did you hear them? An acid wash is the go-to fix for all things pool, it seems. And it is appropriate if done exactly right, and for a very slim (IMO) set of circumstances. I would not qualify your issue as one of those. Here's the rub: acid washing works by dissolving mostly everything in which it comes in contact with, including your brand new surface. It doesn't magically attack the unwanted things and leave the plaster alone. And as often as not, it doesn't even attack what you don't want, but rather burns off the underlying plaster and takes the unwanted stains with it. Some solution, right? And that's if the wash is done correctly, which is not always the case with pool guys.
So if your pool is old, and badly stained, and a year or two away from a complete resurfacing, then yah, an acid wash can clean things up a bit to postpone the inevitable. But on a new surface, all you'll be doing is solving the PB's problem by "spending" some of the longevity of your new surface. Not by a few days or weeks, more like a few years.
So in essence you'll be getting less than what you paid for, because an acid wash will leave less "pool" than you paid for. If your PB suggest an acid wash, then you should either reject the solution, or ask for a substantial return of your money.
You've got an unacceptable pool finish (obviously). If they can't offer a viable solution, then the correct, acceptable solution is to replace the surface (chip it out, reshoot it), at no cost to you.
And while I can't fathom what the actual problem is, it could be just cosmetic, but it could just as likely be a symptom of a bad plaster job, and/or plaster that was not mixed correctly and so is not curing correctly. So any solution that addresses only the aesthetic issue might still leave the underlying plaster problem, which might only rear its head again years from now, outside of your warranty. Until someone of knowledge can definitively say otherwise, the benefit of the doubt should go to you, not the contractor, and the assumption should be a faulty plaster installation until proven otherwise.
I'm a double-barrel kinda guy. I just went through something similar, got a new surface out of it and got the contractor to pay for it. The notion that this is somehow your problem, and that you have to live with it or do with less than you paid for, doesn't fly...