If 'exposure to the common cold at some point in the past' led to improved immune response to Covid then this would be evidence to support your point.
What this article is saying is that exposure to the cold virus at exactly the right point in time helps the immune system fight Covid. That's a small window that isn't overly helped by general exposure. You could even imagine it would be made worse - if we're all exposed to the cold all the time we've developed more immunity and this mechanism might not happen.
Oddly, stating it this way feels like a reasonable explanation for why kids were so spared. During cold season, they are continuously exposed, it seems.
I'm still sceptical of any broad generalization here.
What this article is saying is that exposure to the cold virus at exactly the right point in time helps the immune system fight Covid. That's a small window that isn't overly helped by general exposure. You could even imagine it would be made worse - if we're all exposed to the cold all the time we've developed more immunity and this mechanism might not happen.