B767 CREW HAD A GPWS 'TERRAIN TERRAIN' WARNING TRIGGERED BY HEAVY PRECIPITATION AT 6000 FT OVER THE OCEAN IN SCT CLASS E.

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WE WERE LEVEL AT 6000 FT DURING OUR ARR INTO LAX; BEING VECTORED TO FINAL FOR THE 6L ILS. THE RADAR WAS SHOWING SOME AREAS OF MODERATE TO HEAVY PRECIP BTWN OUR POS AND LAX. WHILE PASSING THROUGH THESE AREAS WE BEGAN TO GET DECREASING RADIO ALTIMETER INDICATIONS AT BOTH CREW POSITIONS. IN ONE CASE THE INDICATION WAS LOW ENOUGH TO GENERATE A TERRAIN WARNING 'TERRAIN-TERRAIN PULL-UP-PULL UP.' ALTHOUGH WE BELIEVED OURSELVES TO STILL BE OVER THE OCEAN; WE RESPONDED TO THE TERRAIN WARNING; CLBING UP TO APPROX 9000 FT. WE INFORMED SOCAL OF OUR ACTION; THEY SAID NO WAY WERE WE CLOSE TO ANY TERRAIN. AT NEARLY THE SAME TIME WE PASSED THROUGH A POCKET OF SEVERE TURBULENCE. SOCAL SAID THAT DUE TO OUR HIGH ALTITUDE THEY WOULD HAVE TO BREAK US OUT AND BRING US AROUND AGAIN. DURING THE ESCAPE AND RECOVERY PERIOD OF TURBULENCE WE MIGHT HAVE EXCEEDED THE FLAPS 5 LIMITING SPEED. WE TOLD THE CTLR THAT IF HE TOOK US AROUND AGAIN WE WOULD LIKELY PASS THROUGH THE SAME AREA OF HEAVY PRECIP AND TURBULENCE; AND WE COULD NOT ACCEPT THAT. WE WERE VECTORED IN CLOSER TO THE ARPT AND THEN GIVEN A SMALL BOX PATTERN KEEPING US E OF THE TROUBLE SPOTS. WE PROCEEDED TO AN UNEVENTFUL LNDG. WE WROTE UP THE SEVERE TURBULENCE ENCOUNTER; THE POSSIBLE FLAP OVERSPEED; AND THE ERRONEOUS RADIO ALTIMETER READINGS AND TERRAIN WARNINGS. ARE THESE NORMAL INDICATIONS FOR THIS ACFT IN HEAVY PRECIP; OR WAS THERE A MALFUNCTION. IT WAS VERY DISTRACTING IN NIGHT IMC/TURB TO GET A TERRAIN WARNING.