After having a public hospital birth with various strangers attending, and a home birth with people all known to me (however, i still had a lot of people in the room - midwife, student midwife, photographer, partner), I agree that any disturbance could hinder the birth.
But the article seems to presuppose that men will ask questions or generally be an annoyance in some way. I think it depends on the man and the relationship. My partner followed my midwife's lead at my home birth. He kept quiet and just made himself useful where necessary (filling up pool, giving me a hand to clutch).
As for trauma, I think that any birth can be a bit traumatic for the parents. I had a perfect home birth - short and straightforward, and even I felt a bit overwhelmed for a few days when I reflected on the pain and the experience. And I'm sure men feel the same, but unless they were particularly sensitive, I'm sure most men can resolve those feelings without packing up and leaving the country as cited as an example in the article. If the man was particularly sensitive or averse to blood or something then perhaps it's best they are not there. I just most adults could cope. I ensured my 4yo son wasn't at my birth though, as I think he would have found it traumatic. even in another room, he would have heard me.
I asked my partner what he thought about the father missing the birth, and he said he wouldn't have missed them for the world, as seeing a birth is the most incredible experience you will ever have.