The answer seems simple to me. In the provided statement the one in question uses I and I'll however never establishes who said "I" owner is and also doesn't establish if he works alone. This leaves room to for the owner to get a shave from party "b". It is unsaid but doesn't quite need to be. You cannot shave someone's hair who has already been shaved. Only shave someone who has not been shaved. Therefore restricting both party a and b from cutting their own hair but not from cutting eachothers.
In the statement I could refer to whomever is running the operation for that day, or even at that time. assuming the time is when you walk in it must have been his day off work 6 rest on 7 .