"...Is this true?"

My guess is that is an attempt by the maker to avoid liability. Seriously, if a horticultural heating mat can't be left unattended - it's useless! I doubt you'd have problems, but you gotta wonder about how much trust you an put into a product which you can't leave unattended. Keep in mind though, that you should be extra careful, whether attended or unattended, using any electrical device around water.

In the past I've used heating pads made for sore muscles. I would recommend that before you sow, you put a thermometer in the soil to make sure the soil temp isn't too hot. If it's above what you want (depending on factors such as what seeds you are sowing) place something to provide a layer of insulation. You can usually even use a couple of pencils to lift it up off of direct contact with the pad or metal pan you described. If try a few things, you'll find something that works well. Again, make sure it's safe.

I use a regular heating pad and place saran wrap over it to keep it clean and dry. The set up is on a metal shelving unit so there's no wood that is flammable. Plus the flat that the six packs are in, has ridges on the bottom so there is no full contact with the whole bottom of the flat. I also have an oscillating fan going on the whole set up, so it keeps the heating pad temperature lower. And the lights and heating pad, are only on from 5am to 7pm at night, about 14 hours. It makes more sense to me, that plants receive similar light conditions to what they would have outdoors.

Thank you both for your comments! What kind of thermometer should I use? I have an instant thermometer for cooking and a regular one for taking someone's temperature - would either of those work? Regarding my normal heating pad, it's vinyl covered inside and has a felt type cover outside of that (snaps over it and can be removed). Would it be helpful to cover the pad and the felt with saran wrap? It is not coming in contact with any water and is sandwiched between two metal baking sheets.

I would use the cooking thermometer. They make thermometers for soil, but I doubt they are any different from one of those cheap analog cooking ones. I don't think an oral thermometer (or the other type lol) is graduated properly for soil temps, but I'm honestly not sure. They are designed for measuring around 100 F.

Some heating pads are waterproof, but as long as what you use will withstand the heat well enough, putting an extra layer around it can't hurt. As long as your soil temps fall into the recommended range for the types of seeds you sow, I don't think you need to be overly concerned, just properly concerned. :-)

My heating pad, is vinyl covered and I have a snap on cover that goes over that, but I felt I wanted more direct contact to the bottom of my flat and I didn't want to get the fabric cover filthy, so I took that off all together and just put a sheet of saran wrap to fit over that before putting the flat over that. Seems to be working fine that way.