RWY INCURSION ASSOCIATED WITH AN UNAUTH RWY ENTRY AND TKOF BY A CORPORATE.

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THE INCIDENT ACFT WAS PREPARED FOR THE FIRST IN A SERIES OF FLTS. THE FIRST LEG WAS TO CNY; UTAH; WITH AN XA00 TKOF. AFTER AN EXTENSIVE PREFLT INCLUDING WT AND BAL; PERFORMANCE DATA; WX CONSIDERATIONS; AND A FACE TO FACE WX BRIEF; THE FLT WAS BOARDED BY 2 PAX; AND BEGAN TAXI TO THE ACTIVE RWY. THE FLTS CLRNC AND FMS LOADING HAD ALREADY TAKEN PLACE ON THE RAMP AT FBO VIA A PWR CART. THE DEP RWY WAS 9L AT OAK. THE ACFT TAXIED WITHOUT INCIDENT; AND JUST PRIOR TO THE HOLD SHORT LINE; THE CREW BOTH BELIEVED THAT A TKOF CLRNC WAS ISSUED AND BEGAN THE TKOF MANEUVER. SHORTLY AFTER TKOF; THE TWR CTLR CALLED US AND INFORMED THE CREW THAT HE HAD NOT ISSUED A TKOF CLRNC; ONLY A HOLD SHORT COMMAND. A FEW MINS LATER AFTER THE FLT WAS STABLE IN A CRUISE CONDITION; THE PIC REQUESTED THAT THE SIC CALL THE OAK TWR FOR FURTHER INFO. MR X ANSWERED THE CALL AT THE OAK TWR AND ASKED WHAT HAD OCCURRED. THE SIC EXPLAINED THAT A HOLD SHORT CLRNC WAS NOT UNDERSTOOD BY THE CREW AND STATED THAT PERHAPS SOME DISTR HAD CAUSED 2 PLTS TO MISS THIS VERY IMPORTANT INSTRUCTION. MR X CONDUCTED SOME INFLT TRAINING WITH US AND ASKED THE CREW ON LNDG TO REVIEW TKOF CLRNC PROCS; AND THAT THE MATTER WOULD END AT THIS POINT.