Well it's official, this is a fictional story with real names. I will now question everything I see for the remaining 7 episodes. I had been suspicous about things for the first two, but last night I went and dug up my 30 yr + copy of Lecke's book.
I had read "Helmet for My Pillow" by Robert Lecke. It has stuck in my mind because in Junior High when I did read it the first time, I was shocked at the behaviour of the Marines in the book. From AWOL, to some purely sick things they did to the Japanese bodies it was completely against the Hollywood depiction of our troops and any other book I had read to that point. Also the people in the book are always referred to by nicknames, never their real name. All in all several things which at the time I thought "odd".
Darn near everything shown last night after they got to the Stadium and left AWOL was fiction. There was no Greek Girl. There were three girls in his time in Australia, the first one he hooked up with, and when he got back to her place she just had a bed in a room and wouldn't do anything until she got a ring on her finger (amongst other things). She thought all Americans were millionaires.. he left in disgust (his words).
The second was a girl, bar maid, one of his buddies was actually seeing. She and he would take walks in the park together and talk.
The third was named Shelia (what else) and he met her on a tram, but she fell into his lap and he wouldn't let her up. They dated (polite word) until she had to go to Tasmania, and then she told him she was married. She showed back up for a single evening months later, then disappeared again.
When he got arrested for pointing the gun at the officer... he and Chuckles (I think that was the guy) had went AWOL to avoid marching in parade. They then stood along the road yelling at the Yanks as they marched by whilst consuming large quantities of beer, a common theme in the book. They faded into the crowd when their buddies showed up and watched them march by from the back. Chuckles had guard duty that night, so he returned to duty, while Lecke remained out. When Lecke showed back up he had brought more beer for Chuckles. After awhile Chuckles excused himself and left Lecke with the gunbelt. The Lt walked up, Lecke pointed the gun at him, screamed about him being a cigar thief and the Lt made a break for it. He returned minutes later with a Cpl and Sgt who snuck up on Lecke and subdued him while the Lt talked to him. Then Chuckles showed back up. It wasn't his "loss" of the Greek Girl which caused this incident.
All in all this is quite sad that they have taken two famous books Lecke's and Sledges and only used them for an outline and characters. Nothing in this can be assumed to be a real depiction of what the people in the books and series saw and experienced.