I've never heard of carpet cleaners recycling water. They usually hook up to an outside hose bib and the water runs through the machine to heat up. If you're having allergy issues, there may be other problems inside the house. Indoor pets? Not changing the AC filter often enough? Wearing shoes inside?
I can't help but give my opinion against ChemDry or any company that sprays foam on the carpet. They are not removing all of it and therefore leaving chemical residue behind. I've posted this before and will do again. The best (3) companies I know in B/CS that do thorough work are:
Boller's Carpet Cleaning
Allstar Carpet Cleaning
Advanced Hard Surface Cleaning
Those companies (or any company actually) can not completely remove ALL allergy causing substances because there are too many other factors outside the carpet cleaners control. Pets on the furniture, in the bed, AC filter issues, nature, etc..
Over the years and reading your bikers on Arrington posts, I think I know about where you live. Nantucket or Indian Lakes. You've probably had your carpet cleaned before. If they're doing a good job, stick w/them. My niece (off Holleman) keeps switching to the next cheapest company and gripes every time.
Hope this helps. One of my buddies works for one of those (3) I listed and I know he's good. Just isn't cheap and doesn't show up looking like an auto mechanic.