I look back on the births of my 3 as the three best experiences of my life, and I would like to encourage you NOT to be terrified 
No one can experience another person's pain, or perception of pain, so it's impossible to say what this woman was going through.
However what others have said about making a conscious effort to stay calm and control your breathing is really really important.
If you panic and start to breath rapidly or hold your breath, your sense of panic escalates because you are deprived of oxygen.
The woman in question said beforehand that she had a low pain threshold and was expecting the worst. I'm sticking my head above the parapet here, but I don't think she made much effort to cope with the pain and reacted very badly from the beginning - screaming in a way that many/most women might only do when experiencing the most intense contractions during transition.
Because her breathing was all over the place, she became increasingly out of control - eg trying to climb off the trolley whilst in transit. I think she just gave in to what she was expecting to be a terrible experience, when it could have been so much more positive.
I'm NOT saying that it doesn't hurt, or that everyone who has traumatic labours could have avoided it simply by staying calm - of course not - but simple things like focusing on slowing down your breathing can help so much.
The other thing that would have really helped her would have been to get off her back and move around. I could not understand why the midwife didn't get her off the bed. I cannot imagine going through a labour lying down, or without the option of someone (DH, midwife) rubbing my back during contractions.
Sorry, rant over 