Keep in mind most low cost spay/neuter clinics don't do bloodwork, fluids, monitoring, etc like a regular clinic, so there is more of a risk. Of course there's a risk with any anesthetic procedure, regardless of where you get it done, but the risk goes up if the "extras" are cut out. Also, if they do a lot of surgeries, things may be hurried and not done as well as they should be. I know thew humane society here uses hydromorphone, but they inject it IM, which usually causes vomiting. Why do they do it? It's faster, and can be done by one person. At the clinic I work at, we give hydromorphone, but we give it IV.
Heck, I wouldn't even use a non-AAHA clinic, personally.
Also remember that some clinics do have an income cutoff. The one here is for families that make $40,000 a year or less. The humane society will also do it fairly cheap for people with 3 or more intact animals, regardless of income.