I think most of it is that people who go to mediums generally want to believe, so if they say general things then people will twist it into their situation.
How many of the below could you twist into saying it's you?
You have a dd who has brought joy into your life.
There is something red that has particular significance to you.
In your house there is one room that feels colder than the others.
In 1999 there was a significant event.
Your mum has had health issues which are resolving.
Three is an important number.
You have an item of clothes that is meaningful to you, but you should throw away.
You have had a promotion at work.
All of which I have totally made up. Then if you want to believe, you twist and I suspect often add the bits in themselves. So for example on the first one, they start saying "you have a dd..." and the person gasps and says "how did you know, I have a dd and I have a..." Medium jumps in with "and you also have a son who is about to do something important" and the person thinks "oh yes, he's going to secondary school next year..."
strangerthongs did it not occur to your dm that the friend might well have given most of the information.
"I'm hoping to come with a friend, she's a bit sceptical but it would be really good if you could help her as she's a bit worried about her dad who has breathing difficulties. It's hard for her mum because she sometimes struggles with the English medical terms. Of course it depends on whether she can get a babysitter, as she's got two small daughters..."
I think mediums are a mixture of broad predictions that people twist into their own situation (let's face it, most of the people they talk to want to believe) and people who are quick on the uptake.
On the big theatre ones I suspect they have paid people mingling before the show and noting things down (Person in the green jumper in the second row is worrying about her baby as it's the first time she's left them with a babysitter).Things that people say in small talk-or even things they hope the medium will tell them ("I'm here because I'm hoping he's got a message from my dm who passed away last year")