A couple of years back PADI issued a statement along the lines that their instructors could sign off on URS referrals, but the referrals would go back to their originating instructors and there would be possibilities that if the originating instructor caused issues with the certification (not sending in paperwork to their agencies, etc) one might find themselves caught in the middle of a situation they could not correct.... in essence, sign off at your own peril was how I read it.
I talked with SSI representatives at DEMA at the time and they said just sign off, wink wink, don't know if that was the official word though. I've had some SSI/NAUI instructors tell me they wouldn't mind if I signed off on their students, others have said no way letting a PADI instructor getting involved.
If one is thinking about using a non-participating instructor to finish off without doing the PADI crossover others have mentioned earlier, they better clear it with the instructors on both ends of the training ahead of time so everyone's on the same page. I used to sign off with the originating instructor's knowledge, but then one time a NAUI instructor sent a student with absolutely NO referral paperwork. I called him and he said he didn't have any, asked me to just set the kid up with a PADI cert. I had to basically turn the student away unless they took the entire course from me, because with NO paperwork, no proof that I was even talking with a legit instructor, it'd have been a complete do-over for the student. Unfair to the student, unfair to everyone as far as I'm concerned. I tend to not want to deal with that again and shay away from doing referrals from outside agencies.