As a person who's worked for one of the largest computer makers in the world I can safely say that no major brand computer company would question you about what you plugged a computer into if it fried...they're much more concerned with your safety. If they're not, buy from somebody else.

Most notebook computer supplies are designed to be pretty robust these days. The premise behind a notebook is that you could be anywhere and plugging it into anything. With the exception of some high end power hungry models, they're pretty forgiving in my experience.

A desktop model is another creature all together. Power supplies in desktops are pretty standard and the basic design hasn't changed much in a long time. Unfortunately this is a common area for cost cutting. That said, I'm not surprised about the warning on desktops. A computer you build yourself would be much more tolerant especially if you installed a top of the line power supply.

If your goal were to run a desktop off of solar power exclusively (don't laugh, you can already buy such things retail) you could build your own computer and then get a DC-DC conversion power supply designed for use in car based PCs. A small battery and some solar panels later, you'd be in business no inverter required. And these power supplies are usually about the size of a candy bar because there's no transformer needed...it's all solid state.