Refiners,
FYI, the "Peoples Pulpit" was an early name for the publishing corporation. It was not an outside group. This is documented in the Divine Pourpose book.
IMHO, I think that Rutherford was using the Finished Mystery as a way to later discredit Russell.
I also think that the Watchtower's Admissions were a way to discredit the "bible students" that continued on after the split when Rutherford took control. Remember, that it wasn't until (about) 1935 that the "Jehovah's Witnnesses" Name was adopted, until then the IBSA, the Bible Students, the "Peoples Pulpit Association", etc... were all one and the same group. When Russell died, many of the original members of the "Bible Students" chose not to follow Rutherford.
So, the Watchtower's admissions were really more of an admission that early writing were "not inspired", and then they try to muddy who wrote/published them as well.