You can read the entire history of the 39th on the main site. The 39th were at Anzio. There is no doubt about that.
I think you may have misunderstood, Theron. He is saying that Anzio is listed as a credit.
There full and actual credits were:
39th Engineer Combat Regiment
D-Day Landings
Gela Sicily
Naples-Salerno
Anzio Italy
Campaign Credits
Sicily
Naples-Foggia
Anzio
Rome-Arno
Po Valley
North Apennines
And please note, that the 39th did not change designations until two months before war's end. They were known as the 39th throughout the war. Again, please read the history from the page referenced above. The 39th's history is taken directly from archives, books and from direct stories and articles written by the men, one of them included is Col. Stanley W. Dziuban, a noted historian for the unit.
Lineage and History
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"