Clearly this guy, as he says, is not an expert. Quite the opposite, I would say!
First of all, any fuse should be able to carry its rated current essentially indefinitely at normal ambient temperatures. The fact that his first 100A fuse test blew the fuse in quite a short time at 100A is a big red flag. Likewise the breaker tripping in similar fashion.
One thing wrong with his methodology is he doesn't understand the implications of employing an inverter. If a "true" sine wave inverter, it will likely be drawing a current from the battery that looks like a full-wave rectified 50 or 60Hz sine wave. That is, the average and RMS (heating effect) values of the current will be different. I'm guessing his meter is average-responding as I did not see "true RMS" labelled on it. Roughly speaking, you could expect the RMS current to be 1.11 times the average value for this case - not a big correction, but you absolutely need to use a RMS reading meter for this (and not just any RMS meter, but one that correctly computes the true RMS value of DC plus AC current). And especially if you don't know the inverter characteristics ("true" sine wave, or modified sine wave, for instance). Here I'm assuming the inverter is connected to a resistive load (as I would expect the heaters to be - although not if they employ phase-controlled heating adjustment). But his power supply charging the battery will likely draw a current with a very peaky waveform, making matters much worse.
Another big red flag is that he expects a fuse to blow quickly even moderately above rated current. The Victron fuse looks like a MEGA fuse. (In fact, I think I can see "MEGA" written on the package label.) Assuming it's from the 32V series, looking up Littlefuse's time-current curves at
you will see that a 100A fuse will trip at about
1.2 seconds for 300A
9 seconds for 200A
about 100 seconds for 150A (hard to read the graph at this point).
So I would say his test (given the major uncertainty relating to not measuring RMS current) roughly confirms that.
Why the other fuses and the breaker trip much sooner, I don't know.
In fact, you actually
want a fuse or circuit breaker to pass much greater than rated current for a short time.
First of all, the things you are protecting can generally handle much more current for a short period than continuously - that includes things like wiring, transformers, motors, etc. Typically the most "sensitive" items are semiconductor devices, which may require special fast acting fuses for proper protection.
But not only can most things handle more current for a short time, they may actually
need to draw much more current during startup, etc. This applies especially to motors, but also to incandescent light bulbs, transformers (inrush current), rectifiers with large filter capacitors, etc.