For the most part, the flat surface of an EPDM rubber is solid and won’t leak. Where most leaks happen is around skylights and vents.
The seams are the problem for EPDM rubber roofs. You will notice that a type of caulk is used called a lap sealer to seal all the seams. That is the prevent water from leaking in from the seams. That indicates then that the glue that is used to glue the seams together can not be trusted to be water-tight.
Waterproofing and Leak Specialists