I have always been given the impression that most cases getting cut with a sword (as opposed to a small knife) usually means you are going to die anyways.
Well, there is that.
But, seriously, I think his point was more about getting over the fear of being cut. I've watched people trying to execute weapons take-aways over and over and the biggest
mistake I've seen is overavoidance. Either moving too far (allowing a very fast follow-up attack) or moving too soon (allowing the attack to be changed). Second is the moving too late which appears - in most cases I've witnessed - to be motivated by fear, just like the overavoidance. It almost seems to be overcompenstation for a tendency to overavoid.
What's more, in my own practice the most common criticism I hear is - yep, you guessed it - overavoidance. And what's it motivated by? Yep, fear.
You don't have a lot of room for mistakes when faced with a blade (none, really). And that fear seems to be a huge source for mistakes. So getting used to the idea that being cut is not necessarily the end of the encounter and being afraid of being cut can get you killed is - in my mind - an important aspect of being able to successfully deal with a knife (or sword) attack.
Mind you, the cases where I definitely
know someone defended themselves against a knife attack they didn't, in fact, get cut. Although, in the one case the attacker suffered first a broken arm, then (when he picked up the knife in the other hand and attacked again) a fatal stab wound to the kidney.
Which is the other half of the cautionary tale: if you're going to use a weapon, make sure it can't be used against you.