The wx at our dest was cavok. At our first alternate it dropped to just below npa minima for a cat 1 airport. But still way above cat 1. The cmd nominated a new alternate above planning minima but we had a little chat afterwards if we could have gone to our first alternate in case we needed to. It was a discussion that arose due to real circumstances but not a question of aircraft safety and airmanship.
Assuming that your ops manual doesn't have anything to the contrary, then legally you could have continued to your destination without any replanning. In fact, you could probably do so even if your destination were zero-zero. EASA has made a concerted effort to avoid "and/or" of late -- this one appears to have slipped through.
But there is, of course, an imperative to do something that is sensible as well as legal. Planning minima are set for a reason -- because forecasts are not perfect, and your skipper was clearly doing something that made good sense as TEM.