I agree with all the comments above.
Seriously, NOTHING removes 100% of the soil/bacteria/spores etc. Carpet cleaning is not sanitizing the carpet. It just makes it more sanitary.
So if your competitor is selling them on SANITIZATION - call them out on it. They're fibbing to your customer.
OK, now that we've established that your competitor is pushing their buttons in a not particularly honest way... Let's bring your service onto the table with them. Have they been satisfied with the appearance, the price, your company's performance, etc.? Would they consider trading your 3 years of good service for a company who is making exaggerated claims out of the gate?
I think that if you'll attempt to reason with them like this, they may be helped to see that you have provided them with a totally suitable service that matches their needs and their budget. Who would want to risk losing that?
My advice is to sell them on CLEAN CARPET. You're the expert. You have all methods at your disposal. And you're in the best position to expertly evaluate which method will work best (albeit encap, HWE, whatever).
Stop selling your customers on "method". Sell results instead. Sell them on your professional approach to customer care. Demonstrate how great their carpet will look on a day-in day-out basis. Sell them on no more recurring spill stains. Sell them on quick dry times. Sell them on a maintenance program that's tailored to their needs and their budget. (All possible with a well implemented encap program).
If some chump is breathing down your throat to try to steal your account, it's time to respond in a positive way to your client. Help them see the value your service brings to their company! And help them recognize that this competitor is blowing smoke about sanitizing their carpet.