Cheapie fuses are notoriously random when it comes to their performance. Grab a random selection and throw a milliohm meter on them and it's more or less a lottery as to each fuse's value.
Given the random variation in cheapie fuses they may just be covering their arse with lower labelled fuses to account for them randomly having a rating greater the label Fuses don't fail straight away even on a modest over current so a short draw of 800 watts may let the fuses survive and that's what they are basing their statements about not blowing on.
It could be that the inverter doesn't have the ratings claimed too. It sure wouldn't be the first time an inverter seller &/or manufacturer has enhanced the rating of the device with nothing but a different label. This might get some people's nose out of joint but it's a fact of life with a lot of these inverters. The Powerjack range is well known for being ludicrously over spec'd on paper, 3 or even 4 times over.
This looks like a classic direct HF inverter. The 1600 watt surge rating is likely relying on a very very brief high current draw from the inverter's high voltage rail capacitors. Usually we are talking 40ms, essentially not much use.
Cartridge fuses come in sizes far greater than 15A. They use multiple fuses because it's cheap. Cheap fuses, cheap sockets, thinner copper on the PCB, you name it. It's all in the name of doing it cheaply.
Do I sound grizzled and worn? Yes, I am
This sort of problem is quite common with this class of inverters and something I've seen myself more than once.
*various edits have been made to this post*
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For a couple of decades the
Buss fuse corporation was my constant companion. Nowadays, there is a better chance than not that the great Bussman fuse corporation has subbed it's manufacturing out to the eco wrecking junk producing slaves of the Pacific rim, but, hopefully Buss is present in the slave factories to assure that quality standards be met instead of wholly discarded. http://www1.cooperbussmann.com/6/AutomotiveandHardwareCatalog.html