i think you are more or less correct, however, in my experiance most custies dont mind paying a bit more if they feel that they can trust you.
we picked up 1 job recently from a recommendation, we went and quoted, the price we gave was approx 1/3 more than they were already paying but they said yes because they 'liked the look of us'.
we turned up a few days later to clean and they told us that 4 more of their neighbors wanted us to clean theirs too. None of them were unhappy with the service that they had been getting from the other cleaners but thet all felt that they looked 'dodgy' and there was 'something they just couldn't put their finger on'.
so be polite, tell the truth, treat them as you would want to be treated and most but not all custies will not mind paying for that peace of mind