I don't think so. Anger is primordial trait of humanity. If it made you dumb we would not have evolved into the intelligent species we are today.
I think the author of the article is confusing anger with someone being mean. He mentions don't be angry with the guy on the other end. Why not say don't be mean to the guy on the other end but let him know that your not happy/angry/upset.
The emotional and rational aspects of the brain are separate, almost competing. The first thing you learn in combat training that's worth a damn is that being hot on emotions and/or adrenaline makes you illogical. People do stuff they later said was incredibly stupid. This is also said by many perps of domestic violence where anger kept building until the urge to attack was uncontrollable. Logic just wasn't there anymore because that's not where logic comes from.
We're taught to recognize we won't have as much self-control, train ourselves to avoid letting emotions control us in an encounter, spend times when we're calm to prepare for likely situations with rehearsed reactions, and defined points when we stop attacks. The combination of these, esp with repetition, lets us handle a highly stressful and illogical situation with low risk of permanent consequences. An ability almost nobody in these classes started with.
Same is true in customer service, management, etc where you're dealing with stress, anger, and/or uncertainty. Same principles. The customer service people most of all since they deal all day with people saying or doing things that would piss them off. By not getting pissed, they keep customers, get paid, and keep their companies from loosing customers. So, the principle to avoid acting in anger where possible just keeps showing up with financial losses or jail time avoided many times over by following it.
I think the author of the article is confusing anger with someone being mean. He mentions don't be angry with the guy on the other end. Why not say don't be mean to the guy on the other end but let him know that your not happy/angry/upset.