CLEARED TO DESCEND TO FL350 COPIED AND SET IN ALT ALERTER FL340.

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ABOUT 30 MI E OF PMD VOR ON J65 AT FL390; WE WERE CLRED DIRECT TO PANOCHE VOR (PXN). SHORTLY AFTER ENTERING OAKLAND ARTCC AIRSPACE; APPROX 50 MI E OF PXN; WE WERE CLRED TO FL340; WHICH WE READ BACK AND SET IN THE ACFT'S ALT ALERTER. I BEGAN THE DSCNT. WE RPTED LEAVING FL390 AND COMPLETED THE DSCNT CHKLIST TO THE 18000' ITEMS. MY COPLT THEN CHKED OFF CENTER FREQ WITH ME TO GET THE OAK ATIS AND CALL FBO TO ADVISE THEM OF OUR ETA AND CHK TO SEE IF THE AMBULANCE THAT WAS TO MEET US HAD ARRIVED. HE CHKED BACK ON FREQ WITH ME AND READ ME THE OAK ATIS. OAK WAS RPTING CLR. I TOLD HIM I WANTED TO FLY THE OAK 27R ILS AND THEN SIDESTEP WHEN VISUAL TO RWY 27L BECAUSE IT WAS LONGER. THE SAN FRANCISCO BAY AREA HAD ALREADY BEEN VISIBLE TO US. INFLT VIS WAS OVER 100 MI AND NO CLOUDS WERE VISIBLE. OAKLAND CENTER ADVISED US OF XING TFC AT OUR 1 O'CLOCK POS; ABOUT 10 MI; LEVEL AT 330. WE SIGHTED HIM EASILY AS HIS RECOGNITION LIGHTS WERE ON. OAKLAND ALSO ADVISED HIM OF OUR POS. I'M NOT CERTAIN WHETHER WE TOLD OAKLAND WE HAD OUR TFC IN SIGHT. DSNDING THROUGH FL347; CENTER ASKED US TO VERIFY 'LEVEL 350.' MY COPLT AND I LOOKED AT EACH OTHER DUMBFOUNDEDLY AND THEN AT THE ALERTER. AFTER A PAUSE; I REPLIED 'NEGATIVE.' WE WERE DSNDING TO 340. CENTER REPLIED 'MAINTAIN 350.' I IMMEDIATELY STARTED A CLB AND RPTED LEAVING 345 FOR 350. SHORTLY THEREAFTER; CENTER ADVISED US OF A POSSIBLE ALT DEVIATION AND GAVE US THEIR PHONE NUMBER TO CALL AFTER LNDG. MY COPLT AND I BOTH REITERATED TO EACH OTHER THAT WE HEARD OUR CLRNC TO FL340; READBACK 340 AND SET THE ALERTER TO 340. THERE WAS NEVER A MOMENT THAT EITHER OF US DID NOT BELIEVE WE WERE CLRED TO FL340. THE REMAINDER OF THE FLT TO OAKLAND WAS W/O ANY FURTHER INCIDENTS. I CALLED OAKLAND CTL AND TALKED TO SUPVR WHO TOLD ME WE HAD BEEN CLRED TO FL350 AND A PLT DEVIATION RPT WAS BEING PROCESSED. THE ENTIRE FLT WAS ROUTINE OUTSIDE OF SOME WX DEVIATION UPON DEPARTING PHOENIX. THERE WERE NO DISTRS OR ABNORMAL OPS. EVASIVE ACTION WAS NEVER CONTEMPLATED NOR TAKEN AS OUR TFC WAS IN SIGHT BEFORE AND AFTER DSNDING THROUGH FL350; AND IT APPEARED WE HAD AMPLE SEP. ALL ACTIONS WERE VERY ROUTINE.