I agree those sleeve underneath the fuse is that's smth. what you immediately pay attention to. Not the best design decision. Though while fuse is not blown the potential here on fuse holder clamps is about a couple of mV to the ground due to fuse extra low resistance. So no ways arc can arise here. The only way for arc to arise is to measure high voltage circuits (lets say more than 1kV) and high energy at the same time in order to blown the fuse (lets say more than 30A). Then yes that dangerous voltage would potentially trigger an arc to the battery leads. What voltage we need here to go through sleeve and through battery leads insulation? I guess more than 10kV. I've seen some test on youtube for that particular case (see below). BTW working with so high voltage/energy is out of scope for this meter, its even not a cat. IV I guess.
The cat ratings are for operator safety: it means the meter has been designed to be safe on circuits of a given type and voltage, by complying with requirements for transients. (E.g. CAT III 1000V and CAT IV 600V both require testing against 8000V transients.) By “safe”, we mean that no harm will come to the person using the meter.
It does not mean the meter itself has to survive. Fluke’s entire reputation (and ability to charge high prices) is based on safety in industrial settings, so if they say a product is CAT III 1000V/CAT IV 600V, then it is, and they’ll have had this independently tested.
As for Joe’s video, I want to say that there have been other reports of the same meter surviving similar tests. I think even Joe himself has said something to that effect. (If he’s listening, maybe he can fill us in, my memory on the issue is spotty.) Either way, the meter failing does NOT constitute a failure of the cat rating.