PLT OF TWIN CESSNA ON THE GND AT LVK ARPT WITH A DEP WINDOW HEARS AN MO21 PLT ANNOUNCE HIS POS ON THE LOC INBOUND.

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I WAS CLRED FOR TKOF AFTER RECEIVING A CLRNC VIA TELEPHONE FROM BAY APCH. THE CLRNC TIME WAS XA38Z AND VOID IF NOT OFF BY XA50Z. DURING TAXI; I MONITORED CTAF. TIME NOW XA45Z. I HEARD ACFT Y ANNOUNCE HIS POS ON THE LOC LNDG LVK. THIS IS THE SAME AIRSPACE I WAS CLRED TO DEPART. I ANNOUNCED TO ACFT Y MY CONCERN WITH HIS APCH AS I WAS CLRED TO DEPART MYSELF. I REASSURED HIM THAT I WOULD HOLD SHORT OF THE RWY AWAITING HIS ARR. HE MENTIONED HE WAS CLRED FOR THE APCH BY STOCKTON APCH. HE FURTHER SAID STOCKTON APCH TRIED TO CALL HIM BUT HE WAS UNABLE TO MAKE CONTACT AND CONTINUED WITH THE APCH. HE ASKED ME TO CANCEL HIS IFR WHEN I BECAME AIRBORNE. LIVERMORE TWR WAS NOT SCHEDULED TO BEGIN OP UNTIL XB00Z. A FEMALE TWR CTLR ANNOUNCED THAT SHE WAS AWARE OF THE SIT AND SHE WAS IN CONTACT WITH BAY APCH. SHE MADE NO FURTHER XMISSION THAT I HEARD. ACFT Y LANDED AND CLRED THE RWY WITH NO FURTHER INCIDENT. I VISUALLY CLRED THE AREA AND ANNOUNCED MY INTENTIONS TO DEPART LEAVING WITHIN MY ALLOTTED TIME. AIRBORNE; I CONTACTED BAY APCH. I CLBED ABOVE THE UNDERCAST AND CANCELED MY IFR REMAINING WITH CTLR FOR ADVISORIES. THE APCH CTLR ASKED ME TO CALL BAY APCH BY TELEPHONE UPON REACHING MY DEST OF VISALIA; CA. I SPOKE WITH TRACON CTLR. THIS WAS THE CTLR THAT GAVE ME THE CLRNC OVER THE PHONE. HE FIRST SPOKE TO REASSURE ME I DID NOTHING WRONG. HE CLAIMED STOCKTON APCH GAVE HIM BAD TIMES FOR MY DEP WINDOW. I ASKED IF EVERYBODY INVOLVED WERE FILLING OUT THEIR NASA ASRS FORMS. I DO NOT REMEMBER HIS ANSWER. IN CONCLUSION: THE SYS FAILED. I WAS FORTUNATE ACFT Y ANNOUNCED HIS INTENTIONS AND I HEARD IT. IT IS IRRELEVANT THAT THE TWR CTLR SPOKE AS THIS COULD HAVE OCCURRED ANYTIME DURING THE LIVERMORE CTL TWR HRS OF NON OP. THE BREAKDOWN IN THE SYS APPEARS TO HAVE OCCURRED IN COORD BTWN STOCKTON APCH AND BAY APCH. FOR ALL OF THE OBVIOUS REASONS; THIS COULD HAVE HAD DISASTROUS RESULTS. AN RCO AT LIVERMORE IS WARRANTED.