Those are official situation maps and the website has some good photos too. I didn't get through all the history accounts there yet but the Allied Counterattacks section says: "The commitment of two regiments of the 45th Division in the 1st Division sector resulted in a depletion of VI Corps reserves. To offset this loss the 36th Engineer Combat Regiment took over a portion of the Moletta River line, relieving all but one battalion of the 157th Infantry. Although the engineers had had no experience as infantry and were badly needed for construction of defenses and road maintenance, by holding a relatively quiet portion of the front they released infantry troops needed to bolster the critical central sector. In the succeeding weeks while the regiment continued to maintain the Moletta River line the engineers were to prove themselves able to handle machine guns and mortars as capably as they handled bulldozers and road graders."
However, the 36th ECR did have some experience as infantry during the prior Salerno operations. There are contrary accounts in details of the regimental history when you study the Adjutant's history, Gen. Gardes' Salerno report, Gardes/Chubbuck interview, personal accounts, and situation reports, etc. Many gray areas still remain.