I retold a story recently on one of the forums about a job I did in a student let. I vacced, pre-sprayed, agitated and freshwater rinsed. It was hard going and I wasn't particularly pleased with my results. So I repeated the wet side of the process. Much better. When I returned to the kitchen for some more water, I found some One Step in the measuring jug waiting to be added to my sprayer
So freshwater cleaning is viable if the circumstances are right.
Another approach is as Doug suggested, but presented in a different way.
"Yes madam, I can clean your carpets by pre-treating with a food additive type of salt and rinsing it away with tap water"
Some people think of CD as being chemical free. I don't know the chemistry involved, but both water and CO2 are chemicals, and everyone (except CD) are trying to use less CO2, not more
And NEVER use the word CHEMICAL. Say Cleaning Solution
Dry Vaccing is technically cleaning the carpet.
Sonic cleaning has been tried but not practical.
Safe and happy cleaning
Ken
PS Why not ask her which article she was reading?