However in small to mid sized enterprise software companies with average developer talent it’s important to keep boundaries (and blame) clear.
In the scenario in question, the CTO will blame OP and make them work the weekend to diagnose/fix it, so wrapping the other exception and throwing their own SomeModuleException will cover their ass.
Java is popular for all the wrong reasons. Believe it or not there are hundreds of such companies in the US alone heavily using Java in this manner and then there is the whole offshore development segment.