Well, what they believe conforms to what you believe about them and I assume you believe that everybody's experience is created through their beliefs. So even if you believe that other people are just reflections of you, you still feel that they are real and not just human robots. And so you assume that the same rules that apply to you apply to them as well.
For example: I believe that my mother is negative and is pretty good in making herself miserable. Her beliefs fit with that so that she creates experiences that fit in with my beliefs about her. When I started with LoA, I had some hope for her and suddenly, things shifted. She said things she normally never had said. But then I went back and she was back to normal..lol. But I have also experienced moments when my belief was directly opposed to hers. Guess who "won"? In those situations it became clear to me that what others believe doesn't matter as long as I don't let myself be affected by it. I cannot know for sure of course what she believed, but I heard her words and saw her emotions and I don't think she felt differently or a little more hopeful inside. But she was wrong in the end. I kinda saved the life of one of her friends, because I didn't believe he was dead, just because a letter came back.

You make a good observation about this statement. Everything we observe and give meaning to in based on our own beliefs and perceptions.

When Agnes say this, she is asking you to take you new adopted beliefs and find evidence for it by looking at others. Personally I think this is a wrong approach because you don't know what another person thinks feels or experiences. So when you do this you will look at another's situation and make a judgment based on your belief of what is going on in their life. But that assumption is your truth not theirs.

So yes you are right, you are using your beliefs to see what you want in others.

Everything we look at and make judgement on is in relation to our setpoint. So if you are wealthy you will look at someone with no money as poor. Further you will say that they are projecting poverty thoughts etc etc. Yet if I'm much richer than you I would say you are projecting poor man thoughts. But in both cases the level of poverty/richness is proportional to one's belief of what poverty or richness is.

So really in my opinion it's of no benefit to look at and make anayalsis or judgements on what others are projecting because you don't know.

Once I was listening to Abe and a audience member asked why if Oprah is so successful and has a good knowledge and application of deliberate creation, does she struggle to lose and maintain weight loss. Hicks replied that Oprah has resistance to weight loss and essentially that's her Achille's heel.

Now another person could say well how do we know that Oprah isn't using wieght loss/gain as a further income stream. It could be a business model she has created. Which is more likely, well only Oprah knows?

I would avoid looking at others and giving meaning to what is going on in their mind - because we are complex beings with mental construct that run deeper than current thoughts.

One thing as humans we do very well is finding evidence in our environment to reinforce our beliefs and sometimes this is positive and sometimes negative.

Spend the time looking at your life and the patterns in your life and work on those.