A small anecdote. An acquaintance related a story of fixing the 'drainage' in their back yard. They were trying to grow some plants that were sensitive to excessive moisture, and the plants were dying. Not watering them, watering them a little, didn't seem to change. They died. A professional gardner suggested that their problem was drainage. So they dug down about 3' (where the soil was very very wet) and tried to build in better drainage. As they were on the side of a hill, water table issues were not considered. It turned out their "problem" was that the water main that fed their house and the houses up the hill, was so pressurized at their property (because it had maintain pressure at the top of the hill too) that the pipe seams were leaking and it was pumping gallons of water into the ground underneath their property. The problem wasn't their garden, the problem was that the city water supply was poorly designed.
While I have never been asked if I was an engineer on the phone, I have experienced similar things to Rachel in meetings and with regard to suggestions. Co-workers will create an internal assessment of your value and then respond based on that assessment. If they have written you off they will ignore you, if you prove their assessment wrong in a public forum they will attack you. These are management issues, and something which was sorely lacking in the stories.
If you are the "owner" of a meeting, and someone is trying to be heard and isn't. It is incumbent on you to let them be heard. By your position power as "the boss" you can naturally interrupt a discussion to collect more data from other members. Its also important to ask questions like "does anyone have any concerns?" to draw out people who have valid input but are too timid to share it.
In a highly political environment there are two ways to create change, one is through overt manipulation, which is to collect political power to yourself and then exert it to enact change, and the other is covert manipulation, which is to enact change subtly enough that the political organism doesn't react. (sometimes called "triggering the antibodies").
The problem with the latter is that if you help make positive change while keeping everyone not pissed off, no one attributes it to you (which is good for the change agent because if they knew the anti-bodies would react, but bad if your manager doesn't recognize it). I asked my manager what change he wanted to be 'true' yet he (or others) had been unsuccessful making true, he gave me one, and 18 months later that change was in place. He didn't believe that I was the one who had made the change. I suggested he pick a change he wanted to happen and not tell me, then in 18 months we could see if that one happened :-). But he also didn't understand enough about organizational dynamics to know that making change without having the source of that change point back at you was even possible.
The point is that one of the very important jobs of managers is to make sure that people who work for them are contributing as much positive to the company as they can, and when they are being held back from that contribution by people who are oblivious, willful or otherwise, they jump in and fix that.
Just another way that "managing" is different than "engineering" I suspect.
I have used the following to provoke thought and discussion around problems in a way that does not call anyone out:
Ill recap the decision, design or plan. Putting it on the whiteboard or in print or whatever format the succinct plan is in.
I then ask everyone on the team or in the meeting to look at it and specifically look for why it wont work or what is wrong with the plan.
Not what is wrong with WHO designed what - but tell the team why it wont work.
With the important distinction: Anyone one who brings up a reason why they think it wont work is not only heard, but if their reasoning for why it wont work is incorrect, the team explains why that risk or issue is mitigated by the plan.
For example, you have a design where one person perceives a single point of failure due to X. "well, we'd lose service if this device went down"
Then the team explains "well, actually that doesn't matter because we stay up due to [this design element over here]"
This brings everyone up to speed and educates them as to why the plan is such.
If something is brought up that is a valid miss - then its addressed and a plan on how to redesign for that condition is met.
The point is beat the design to death - not the person or team.
The team is supposed to put all their irons in the fire and forge out a solution together.
If you make the discussion directed toward the manager/team leader, then the conversation is much easier.
Again, the team needs to put all their irons in the fire to forge a decision. The plan/ideas of the team is the metal to be forged. The fire is the funding and backing for the project. The hammer is the effort of the executing team and the tongs are the skill of the overall project management.