In essence you are right it is a CYA statement. Poor quality inverters produce a distorted wave form more akin to what is almost a square wave which contains every odd harmonic of the basic frequency. So a true 50Hz Square wave has 50Hz, 150Hz, 450Hz, 900Hz,
and so on in it in decreasing amounts. In practice they actually produce a "topped and tailed" wave which is missing the peaks and troughs.
There are two main types of power supply to produce low voltage from mains. Linear which feed the mains directly in to a transformer as AC, reduce by a ratio to near the required output then feed it through rectifiers and regulators to produce the feed.
Because the transformer is directly connected to the mains noisy input makes for a noisy output. These are easy to identify because they have big transformers and so are heavy.
The alternative is a switched mode supply and these take the incoming mains and immediately rectify it to produce DC and smooth it with a relatively big capacitor, chop it up to reduce the voltage then also rectify and smooth it again. These use smaller
transformers so are much lighter and are the type used in PCs, laptops and other electronic devices. For example if you made a PSU capable of delivering the power needed for a PC out of a linear design it would weigh several tens of kilos.
Thats the boring bit, more important is should it matter and in essence no. Switched mode power supplies are inherantly noisy electrically speaking so have the components and design to get rid of that noise. There is no difference between that noise and
the noise made by the poor waveform of the inverter so it works for both. Spikes can be more of an issue and are prevalent with generators or starting the car with the inverter in use so a spike suppressor plug/socket might help although most have that circuitry
built in. So in general pay for a good one just a little more powerful than you need instead of a cheap one far bigger than you want.
Some inverters are labelled as "pure sine wave" and these are therefore supposedly the same as the mains supply. They are a little more expensive but for peace of mind look for one of them. Lets face it, the mains is not that clean especially if you are
in a rural location or next door to a factory, perhaps even working in one. I had an installation to do in a workshop that cut steel with a robot that had an electric arc cutter head and the noise that generated was huge.