AN A300 FLC CROSSES THE FAF 700 FT LOW ACCORDING TO TWR CTLR AT GTF; MT.

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RADAR VECTORS TO VOR 21 AT GTF. PRIOR TO THIS; RECEIVED LATEST ATIS PRIOR TO DSCNT: HIGH CEILINGS; RAIN SHOWERS IN VICINITY. BRIEFED VOR 21 (NO ILS THIS RWY; WINDS TOO STRONG FOR ILS ON RWY 3). EXPECTED TO ACTUALLY FLY VISUAL APCH BASED ON ATIS CEILING AND VISIBILITY. APCHING ARPT (APPROX 30 MI OUT) SAW RAIN (GREEN; YELLOW; FEW DOTS OF RED ON WX RADAR). EDGE OF RAIN JUST SE OF ARPT. WHILE ON VECTORS; APCH CTLR SAID RAIN APCHING ARPT FROM E (WE WERE ALSO COMING IN FROM THE E) AND VISIBILITY DROPPING. CLRED FOR APCH APPROX 7000 FT MSL; INTERCEPTING INBOUND RADIAL APPROX 3-7 NM FROM FAF (TRIGG) -- WE WERE ALREADY SLOWED AND MOST OF FLAPS ALREADY OUT. FULLY CONFIGURED AND CHKLIST COMPLETE BY FAF. DEPARTED 4800 FT (FAF ALT) .2 NM PRIOR TO TRIGG (.2 NM LEAD IS OUR SOP) AND RAPIDLY DSNDED TO MDA (4000 FT MSL). PRIOR TO/JUST AFTER FAF IN MODERATE RAIN ALL THE WAY TO RWY; THOUGH ONLY LIGHT RAIN AT TOUCHDOWN. LIGHTNING OFF OUR L SIDE NEAR FAF; ABLE TO SEE GND PRIOR TO FAF; THOUGH DIDN'T SEE VASI FOR RWY OFF OUR L TILL AT MDA (IF NOT FOR BRIGHTNESS OF VASI; WOULD NOT HAVE SEEN RWY TILL MUCH CLOSER). TURB IN DSCNT; MDA THROUGH TOUCHDOWN. FIRM LNDG WITH AUTOBRAKES SET AT MEDIUM. WHY I'M WRITING THIS: EITHER TWR OR APCH CTL (PROBABLY TWR) INFORMED US AFTER WE REACHED MDA THAT THEY SHOWED US XING TRIGG AT 4100 FT (FAF AT TRIGG IS 4800 FT). I DON'T THINK WE STARTED DOWN TOO EARLY; THOUGH I KNOW WE WERE AGGRESSIVE TO GET RIGHT DOWN TO MDA. MY MISTAKES: NOT TRULY PREPARING MYSELF MENTALLY FOR US TO REALLY FLY THE APCH. THIS WAS THE FIRST VOR APCH IN REAL LIFE (AS EITHER PF OR PNF) IN THIS ACFT (2 YEARS). THOUGH WE PRACTICE IT IN THE SIMULATOR EVERY 6 MONTHS (UNDER IDEAL CONDITIONS); I HADN'T SEEN ONE SINCE MY LAST SIM. NEXT 6 MONTH CHK RIDE IS THIS WK!