To be fair, it was not only the Allied pilots who overclaimed. MAW4 reports the results claimed by a raid of a dozen Fw 190s on the harbour: "A large landing craft was reported to have exploded and sank and hits on eight cargo vessels were claimed to have been achieved."
Seen from the Allied side:
British Admiralty War Diary, 27 January 1944
"... L.S.T. 321 was slightly damaged in an air attack today."
"Enemy air effort, judged by the number of sorties, appears to be diminishing. During daylight today, 140 enemy aircraft were reported over the assault area, of which 25 were claimed destroyed, 3 probably destroyed and 5 damaged."
The Official Chronology of the U.S. Navy in World War II, 27 January 1944
German air opposition to landings at Anzio begins to increase; submarine chaser SC-534 is damaged by near- miss of bomb.
Comment: I don't know how this piece of data was added to the chronology, but the war diary of SC-534 is online and for that date they only recorded seven General Quarters alerts and nothing else (see
https://www.fold3.com/image/271077886)
British Admiralty War Diary, 28 January 1944
"Yesterday unloading in Anzio area proceeded rapidly in fine weather. ... Despite rather heavy air attacks on shipping in landing area there were no losses to ships or landing craft so far as known. ..."