R.J.
<grinning> What you need to do is ask for just a steam clean...no "cleaners" involved.
I haven't used them for awhile (have my own machine now), but Stanley Steamers was always more then happy to just use steam (saves them money, but we get charged the same). My husband was allergic to one of the components in carpet cleaning chemicals, his feet would blister if he walked barefoot within a week of cleaning.
The other option, of course, is to spend the same amount that you'd spend on one professional cleaning, and buy your own machine. That way you can use or not use any cleaners that you would like.
After having rented the atrocious RugDoctors and others, I figured steaming my own carpets was going to be a major pain. Imagine my surprise, when the bissel pro heat was actually easier to use than my vacuum! Switches from carpet to tile to wood. You have to empty the dirty water fairly frequently, but the bucket thing was super easy to take out and pour down the toilet (no drips/spills), and fill in the sink.
Incidentally, if you head out the middle east, you'll see that persian rugs are just taken outside, scrubbed with brushes and mild soap, hosed off, and hung to dry. You have to be careful to dry them so they don't stretch...but if you're looking at cleaning high quality removable rugs...that's the other option. Always check for color fastness, and try not to hang in direct sunlight.
Good Luck