That is BS. Excuse me, but it is :D
It could get messy, but doesn't have to be. I set up my whole work stand in the kitchen on top of a wax cloth covered with newspapers (I had to do a lot of other stuff as well), and I had several rags handy to catch spills. You don't want to get brake fluid on your bike because it strips paint (not that anyone would notice on my bikes) but it comes out in dribbles and droplets, not gushes. I wrapped a small rag around the bleed screw at the brake lever which was handy for picking up small spills.
The instructions with the bleed set were a little confusing, but I found a useful video on youtube showing my brakes (Hayes Stoker). Yours may be bled another way, but basically all I did was attach a bottle full of brake fluid to the bleed screw at the caliper (if this falls off it does get messy) and a spill bottle by a hose from the bleed screw at the lever (ditto if this one falls off). Then I just squeezed and released until all the bubbles were out and the system was full of clear fluid.
(My mistake on the first wheel was being overzealous about rotating the caliper to let all the trapped bubbles escape. I rotated it above the hose several times, letting all the air in the hose into the caliper... :o)

