I notice that in hollywood at least that Germans almost always wear their helmets with the chin strap done up, as do the English, but American troops never have theirs done up.

Does anyone know if A: this is historically accurate, and B: if so was there a particular reason behind it ?

No, its not historically accurate and John Wayne was the cause. He didn't like wearing a chin strap in his movies, so he didn't. In reality, if the chin strap is not fastened, you loose the helmet very easily and it doesn't protect your head for long. We still get onto soldiers and ask them "Who do you think you are, John Wayne?" when they don't buckle their chin strap.

I did a Google search for photos

Numerous WW2 photos show US solders without chin straps attached. The same is true for Vietnam. Often, but not allways, when worn the straps are very loose.

Incidently in the movie To Hell and Back (About and staring Audie Murphy, the most decoreted WW2 US soldier) chin straps are rarely seen. I looked at photos from the movie. It has been years since I've seen the movie but I think that in at least one action scene Murphy looses his helmet

My impression from looking at photos:

Germany: Strap under chin
Britian: Strap under chin
Japan: Strap under chin
Soviet: Strap under chin, but often wore other headgear instead of helment.
USA: Strap not generally used but a few photos show some men using strap while most in photo aren't using it. There are also some photos where everyone is using strap

Even in civvy street rules apply to the wearing of chin stays on hard hats,when we were first issued the hats had no straps attached and everyone was recalled and issued with straps and given instructions that they must be worn at all times.Back to my service days have you ever tried running with no strap in place....

I found this link to Normandy photos on World War II Forums ww2f.com

http://www.flickr.com/photos/photosnormandie/

This had nothing to do with John Wayne, but was a product of some unknown G.I. "trench physicist," who came up with the idea that the new M1 helmet (which replaced the British style tin plate at the beginning of the war) could trap air from a shock wave under it in the event of a shell exploding nearby. The theory was that it could snap the wearer's neck if the strap was fastened, and this bit of scuttlebutt spread among US troops throughout the ETO, and green troops were soberly advised of this "fact" by frontline veterans as soon as they arrived. The strap was usually fastened over the front rim of the helmet.
This bit of "wisdom" was not spread in the Pacific, where G.I.'s and Marines continued to buckle their helmet straps. And there was no epidemic of broken necks.

Based on photos, it appears the majority of the US troops in the Pacific used the chin strap while most in Eueope did not.