I agree with you blarg, it sounds like the staff was to a point, pretty absurd. Sometimes they can be that way.
However in the same article you posted it sounds like these passengers may have also been absurd and "cursed and yelled" at the crew with other passengers hearing the ordeal, and also refused to speak to a "team leader.". Why the refusal? At one point the father approached the flight attendants. Again, why? No need for that.
Again, arguing and yelling and swearing is never going to pan out well on a plane, and if the Captain flying the plane says you're gone, well, thems the rules. These rules are made and enforced vehemently. This isn't a bus on a side street, he's going thousands of feet in the air and he's got 200 other compliant people who aren't cursing and yelling that he needs to take care of.
Sounds like a he said she said, but again, as a passenger, things can usually be sedated by a decent attitude and compliance with rules, even if they're not what you think they should be.