Brainstorming: The process of idea generation, generally done as quickly as possible, often in a team so members can broaden their perspectives by feeding off of the ideas presented within the team.
Plotting: Figuring out how a story gets from beginning to end.
Where did these definitions come from? The crowded, noisy insides of my own head. Meaning that yes. I made them up. I did that because I wanted to drive home that these two activities are not the same thing. Nor are they interchangeable. I suspect for most writers (I know I'm one of them) brainstorming precedes plotting. That said, I believe the question was when should someone else help you brainstorm.
My answer: Any time. All the time. So long as it's someone else's work we're brainstorming. Leave my story out of it. Don't get me wrong. I love What-if-ing. I love asking questions about stories, finding the places that intrigue me about it and I love to start lobbing thoughts and ideas around. For anyone but me. Like James, I don't want to examine my ideas too closely when they are newly hatched and still fledging. They're too fragile for examination at that point. I want to sit with them in silence and see what develops. If I'm going to ask for brainstorming for me, it's going to be when I'm at least halfway through the book and 'stuck'. Then all I want is get out of whatever corner I've written myself into.
But plotting. Ah, plotting. If we're going to talk about that, it is important to impress upon you my theory that there are two types of plotters in the world. Possibly more. Regardless. The two types break upon a single point of procedure: Do you decide what happens first? Or do you come up with characters first? (I'm that last one.)
Plot-driven writers seize upon an idea for a thing or a situation. Something like "what if Supreme Court Justices were being murdered to clear the way for new nominees?" (Not that this story idea occurred to me today or anything.) A plot driven writer could lay out the major story points without ever knowing who his or her protagonist was. Characters are slotted in somewhere, but they definitely show up after the plot has started taking shape. These folks usually benefit from brainstorming sessions more easily than their character-driven counterparts because the plot can be anything. It's freer form when you don't pin the plot to the foibles of your characters.
Character-driven writers might get an idea for a situation or for something that happens, but usually, there are characters already attached to the situation or event. Half the time, the characters show up and announce that you'll be writing their story thank you very much. For character-driven writers, brainstorming isn't very useful because these writers require that the plot come from the characters. These are the people who need to know what someone's inner wound is (a question Jeffe mentioned annoys her). These writers have to know what makes their characters tick because it's the places where the characters get stuck that the story starts. For that reason, these writers have to know their characters intimately. Everything that then happens in the story is designed specifically to hammer these characters at their weakest points so they either shatter or they strengthen. Character-driven writers end up elbow deep in the emotional lives of their characters - in fact, they require that - before they can begin plotting. That means that brainstorming with a group of people who don't have the same level of character knowledge just isn't going to work. It'll be an exercise in frustration for everyone involved. Most character-driven writers I know avoid brainstorming entirely, unless they are brainstorming for someone else.
So yeah. That was a really long way of saying, "It depends" in answer to the when should someone help you brainstorm or plot question.