That's ridiculous. How the hell do they screw up something like that? Seriously, what the hell did they do to her?
Don't sign that paper. Call the vets, explain that you want the paperwork to reflect your verbal agreement before you are willing to sign anything. Make them send you a new one.

Frankly, it sounds like an old-country-vet attitude. I've worked at a vet clinic before, and they always wanted to do the spay surgery when the bitch wasn't in heat. When they go in heat, everything is engorged and the dog could easily lose more blood during the surgery. Waiting six months is absolutely stupid.

Call around to other vet clinics and speak with them about the best time to spay, and how common or uncommon it is to botch a spay. Get other opinions and consider just getting a refund on the surgery and taking her to a more competent vet clinic that doesn't act all shady.

Have there been complaints about this clinic?