You need to alter your mindset....
The carpets were different from the first time you cleaned them, why assume it's because of something you've done different?
You don't know what's happended to the carpet in the time between the last clean, just admitting it was your fault and maybe due to using a different chemical was total guesswork
Nothing you used would cause a resoiling problem so the problem is caused by what is in the carpet (which you did'nt put thier so it's not your fault) why apoligies for something that is not your fault?.
You are now working from a position of weakness that it your problem and you did something wrong ....which is not the case. It thier problem caused by them, you are the good guy trying to put it right.