What one customer sees as a service, another might see as a product. As an example, a mobile phone company provides a phone, which could be seen by the customer as a product which allows them to make calls and send/receive text messages, and provides various other capabilities. It could be regarded as a service - being able to make phone calls etc. which just happens to include the supply of a phone handset in order to use the service. Whether the customer sees it as a Product or Service is subjective, and probably doesn't really matter all that much. From a customer's perspective, it's what the Product or Service does for them, the value it provides, which is important. The mobile phone Product or Service allows them to make calls and other tasks - the value is in achieving the outcome, not in buying the product or service. If the customer didn't have the need, they probably wouldn't be buying.
Our industry can be guilty of spending too much time on semantics - is it an 'incident', or should we call it something else? There are an embarrassingly large number of examples.
Surely any organization who wants to be successful, realizes the necessity for understanding this customer-centric perspective. This awareness is absolutely necessary if we hope to design and deliver successful products and services. Regardless of whether we're a commercial organization, charity, not-for-profit, public sector or private, isn't this completely critical?
People have different views, and why should we have the right to dictate how people should think, or the language they use? I would argue this is a distraction, and not massively important. The main point is that a good service provider, or any of us who believe they have any element of service management in what we do, should do everything we can to understand what the customer wants or needs to achieve, and how what we do makes that happen - that's what makes it a valuable service.