I think courting is the more accurate term in this case, but it would have been fine if he had said dating and a lot of people would have used that term. I think courting is probably viewed by some as an old fashioned term because we no longer insist on virginity before marriage as a primary means of birth control and disease control, so we have more latitude for establishing romantic relationships without necessarily planning to marry the person.

So these days you aren't necessarily trying to decide if you want to marry. In Edwardian times, that was more likely to be the goal of seeing someone: to try to establish a serious, committed relationship under the bonds of marriage.

Dating seems to be a broad term that can mean anything from casual hookups to courting for purposes of trying to marry. And the fact that it's broad has two positives to it: It gives the couple latitude to sort their own feelings without deciding ahead of time if this is a casual hookup or a serious courtship (or something in between) and, secondarily, it protects their privacy.

It protects their privacy by allowing them to communicate to others that "We are seeing each other romantically" while sidestepping questions like "How serious are you two?" or "What are your intentions?"

It also protects their privacy by declining to indicate if they just had dinner together or if they actually slept together. And it's not anyone's business in many cases, though people tend to be nosy.

Sometimes, a broad umbrella term that is not making such specifics clear is a feature, not a bug, of using it. But I agree that the broader term would have communicated something different in this case and the more specific term is the correct term for what he likely desired to communicate.

They did get married. Now that he is married, he has no need to obfuscate the fact that he wanted a serious relationship.