Conflict of interest/collusion in academic scenario
If this is a real, rather than a hypothetical, then yes, Joe has been unethical and probably criminal, though it might be hard to make the case. 

In theory you should bring it to the attention of the authorities, but you will be creating a painful situation for yourself, conceivably being charged with slander. An anonymous letter to authorities would be safe, but easy to ignore. 

A group of accusers would be more likely to be heard than an individual. A complaint transmitted by a trusted authority such as a lawyer would be relatively safe and the lawyer could advise you on your potential liability. 

But the charge is a serious one.