Mostlyharmless, I think that by "safe" they mean storage wise, and ease of use. If you are simply putting fuel into a cup, and buring it, that is safer than dealing with a gas under pressure (in theory). If a lit alcohol stove spills, well, you have buring fuel now. But, it will go out relatively quick. And, you wont have flame ups, as you do with most other stoves. Fuel storage is also a little better-although not sure if that would count as safer or not.
When it comes down to it, alcohol stoves are safer than most others, IMHO-the only thing you need to be careful of is knocking the stove over. Almost all others there are numerous issues that can crop up.

I think that this weekend I am going to take all the stoves I own out, and do some field tests. Not sure what the weather will be, but I want to do a comprehesive test. I will try the following:
minibull designs alcohol stove.
homemade CAT stove
canister stove (forget the maker)
wood burning mini paint can stove.
Brass alcohol stove

Will get boil times on all of them, using the same amount of liquid each time. Besides, I need an excuse to get outside