Given that the inverter and static switch are both semiconductor devices, with very real limits to their current handling capability, these devices are capable of being destroyed under fault conditions, so in a very real sense, they are your fuses. (Old saying - its amazing how a thyristor will lay down its life to protect a fuse)
Your customer is showing the right approach - he wants the highest reliability power so wants the minimum number of failure points possible, so no fuses please. Now if that means that if there in the rare case of a bolted fault in or just after the UPS that the UPS simply vanishes off the planet in a puff of smoke, well, thats an acceptable compromise, beacuse at that point the data centre is down anyway, or if its designed right, half down, so no break in customer service.
I have a distant memory that NASA used the same thinking during critical parts of spaceflight - the circuit breakers in the electrical distribution system had either a bypass or mechanical holdin, and during these critical events the breakers simply couldn't open, the thinking being we'll take the fire here rather than loose the facilities supporting the guys off-planet. Unfortunately, I cannot provide a reference for this, but I'm sure I didn't dream it.