That's a pretty solid explanation. There are a million different versions of virtually the same process. The process being smoothing out the bore by shooting the gun, then cleaning, then shooting, then cleaning etc.
Some people shoot 1, clean, 1 clean etc. for the first 5, 10, 15, whatever. Then they'll move to cleaning every 10, etc.
The break-in for every barrel will be different. Some will require more than others. Let the barrel tell you. I believe that a good many shooters spend too much time performing needless break-in cleaning cycles. That's not to say that it isn't necessary, I just think a lot of folks over do it. I've seen situations where guns were not allowed to shoot to their full potential, simply because they were constantly being cleaned. Sometimes a little bit of copper lining is a good thing.