1. About "...either for training purposes.." part of your question. Sure it's legal for 2 pilots to be doing training in a single pilot helicopter fitted with dual controls; the instructor pilot logs PIC time, the trainee pilot logs it as dual time.
2. About "..or just because the boss says so..." part of the question. The boss (operator) appoints a person to be the PIC. If the particular operation requires more than one pilot, and it's specified in the operational documentation as so, and complied with, then the guy who is appointed PIC by the boss logs PIC, the other guy logs co-pilot. Just because an aircraft has one engine doesn't automatically disqualify a co-pilot role if a co-pilot is necessary in the operational context.
I'm not citing any reference to regulation as it seems self evident to me that both is logically so.