Bear in mind that pictures taken away from the front, even in combat gear, is not indicative of what they would have worn into combat. So sure, there were stars there - but he could have easily swapped them out before combat.

Also, as combat wore on, various command started removing external insignia and markings, and prohibiting salutes, for front line units once it became clear that being able to identify your leader in combat was less important than said leader not being targeted.

A quick excerpt online can be found in Mountain Troops and Medics: A Complete World War II Combat History of the U.S. Tenth Mountain Division - A Battle Surgeon's True Stories by Albert H. Meike, here on google, which says on page 47 that they started removing external insignia and markings particularly after they were being targeted.

Note that these lessons - which seem obvious today - often only become common knowledge after incidents happen. Thus, the lack of markings found on combat uniforms for the military today (and prohibition on salutes in higher risk areas) has come about largely from the lessons learned in past wars