It was a question I asked when I first bought one, and they assured me it was OK. (I was unaware of, and there was no mention of, technical floor loadings.) I seem to recall a claim that there were no known instances of floor failure due to a waterbed.
However, your question prompts me to do the maths. Waterbed mattresses typically are 15-20 cm thick. that is a mass of up to 150-200 kg/m2, or ~1.5-2kN/m2. The base designs have a surround and additional cross pieces to make an even spread of load (in the context of floor support), so that equates roughly to the floor loading. There is also the weight of the frame, and occupants, spread over the whole area of the bed support, adding maybe 0.7-1 N/m2. That gives a total load of 2.2 - 3N/m2, so up to double the rating you quote.
Curious, I’ve had a quick look at UK building regs, and current Approved Document A mentions an imposed load of 2kN/m2 (distributed load). Without a copy of the relevant BSs I can’t check further detail as to minimum requirements, or what the position is regarding loads not evenly distributed (much of the remainder of a bedroom would have considerably lighter loading, making the average distributed load much lower).
We’ve had our waterbed in three different rooms, the first a1920s house with an 11’ joist span, the second a 1980s house with a 14’ joust span, and presently in a 1970s house with 13’ joist span. In the first two the floor joists ran lengthwise in relation the the bed, and current room at right angles. In all cases the head of the bed tight to the wall. In none of the houses has there been any evident bowing or cracking of the ceiling beneath, which in the first hose was laths and plaster, the others skimmed plasterboard.
For anyone contemplating, make of this what you will!