Sounds like a fishy story. While PVD Tower (and Approach) do close at midnight local time, Boston Center can definitely issue approach clearances. Whether they have radar good enough to provide vectors to final, that's another story.
APCH/DEP SVC PRVDD BY BOSTON ARTCC ON FREQS 124.85/307.9 (WOODSTOCK RCAG) WHEN APCH CTL CLSD.
I think the issue was more one of extremely low ceilings, not lack of ATC coverage:
KPVD 160251Z 02003KT 1/2SM R05/1600FT FG VV001 13/12 A2990 RMK AO2 SLP126 T01280122 58007
I'm pretty sure that the METAR above (from Monday night) would put the weather below Southwest's landing minimums.