I quite agree with that. With caution, respect of the depth and training...
Comparing as it is done here with dives 40 years ago or more is not fair. When you speak with divers who used to dive at this time you realise sometime the dives were made without much caution. It was a more "dare devil" time, with divers going down to 80 m on air and don't really thinking about it, so of course there were accidents !
Clearly another point is the way we dive in Europe and how it is made in America : in America there are clear distinction between rec dives on ndl at around 20 to 30 m and tec dives (PADI and the other agencies have made their job). In Europe it is a bit different the distinction is not that clear : we have deco dives, sometime we go below 40-45 m, even on air, but don't always think it is tec dives. But many accidents with dives on air in the 50 m range ? Not really. But as David said it is certainly more cautious to dive with something else than air at those depth