CTLR AT PBI DID NOT HAVE PLT READBACK HOLD SHORT INSTRUCTIONS RESULTING IN A SURFACE INCIDENT.

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THE PA28 LANDED ON THE CROSSING RWY 13 AND WAS TOLD TO TURN R ON THE NEXT TXWY WHICH WOULD HAVE BEEN F. THE PA28 TURNED ON THE REVERSE A. I GOT HIM GOING IN THE RIGHT DIRECTION AND WENT ABOUT MY BUSINESS. WHEN THE PA28 WAS ON F I GAVE HIM FURTHER INSTRUCTIONS TO CROSS TXWY C HOLD SHORT ON RWY 9L ON F. HE SAID 'OKAY; DO YOU WANT US TO STAY WITH YOU OR GO TO GND?' I SAID 'STAY WITH ME' AND THEN CLRED THE G3 FOR TAKEOFF ON RWY 9L. THE G3 WAS APPROX 800 FT DOWN THE RWY ON TKOF ROLL WHEN I SAW THAT THE PA28 WAS NOT GOING TO STOP OR HOLD SHORT OF RWY 9L. I IMMEDIATELY TOLD THE G3 TO 'ABORT YOUR TKOF; CANCEL TKOF CLRNC' AND TOLD HE PA28 TO CONTINUE ACROSS RWY 9L; THE G3 TURNED L ON THE NEXT TXWY AND TAXIED BACK TO THE APCH END OF RWY 9L FOR DEP. THE PA28 WENT TO GND CTL AND WAS GIVEN THE FACILITY PHONE NUMBER; HE CALLED AND SPOKE TO THE OPS MGR AND ADMITTED THAT HE MESSED UP. I DID NOT VERIFY THE HOLD SHORT INSTRUCTIONS WERE RECEIVED BY THE PA28. THERE ARE TIMES WHEN YOU CAN TELL BY THE PLTS VOICE WHETHER THEY HAVE TO BE LED BY THE HAND OR CAN WORK SOMEWHAT INDEPENDENTLY; I WAS FOOLED THIS TIME. UPON DOING SOME RESEARCH IN THE AIM WE FOUND THAT PLTS ARE NOT REQUIRED TO READBACK HOLD SHORT INSTRUCTIONS; THIS IS GOOD OP PRACTICE BUT NOT REQUIRED. ATC'S ARE TO REQUEST READBACK INSTRUCTIONS. IT SEEMS TO ME THERE IS A MISSING LINK; THE TWO DO NOT CONNECT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT WHEN THE PA28 WAS INSTRUCTED TO HOLD SHORT OR RWY 9L; HE SAID OK; BUT CONTINUED ACROSS THE RWY. RPTR SAID THE CONFLICT WAS CLASSIFIED AS A SURFACE INCIDENT.