I don't think it is a Rick case; all the Rick cases (Rick Case ) I have seen or owned have longer, rectangular accessory compartments, unlike the one in your case.
When I bought my '72 4001 slightly used in '75 from a guitar store, it came with a case that looks remarkably like that (other than mine is really beat up now). IIRC, it was a new case, not one that came with the bass from the previous owner. The case is very generic. It's also just a bit long for my bass, perhaps designed to accommodate the longer headstocks of earlier 4001s.
So I suspect that is a "case for a Rickenbacker" not a "Rickenbacker case."