Actually, SSI participates in the universal referral program, but PADI as an organization does not. In fact, they are opposed to it because they feel strongly that the instructor who does the OW testing should be the certifying instructor. They see a potential problem if a diver has a skill-related accident after being certified to dive by someone who never saw the diver in the open water.
PADI does, however, allow individual instructors to participate in the universal referral program if they want to. If the PADI instructor agrees to do this, then he or she will use the universal referral process, and the diver will be certified by SSI. If the PADI instructor does not wish to do this, though, then the only real option is to have the PADI instructor give a PADI certification. In that case, some additional work will be required to complete the process, and it may cost a little more.
The safest thing to do is to have the SSI instructor locate an instructor who will officially agree to the universal referral program at the diver's destination.