That is probably true for the vast majority of the 03A3's. But it seems to be well documented that a number of the late 03A3's, having been supplanted by the Garand, went directly into storage. I guess none of us can blame a soldier for wanting a semi over a bolt action.
I've got a nice Remington 03A3 that I believe is in the "direct to storage" category. Of course, I can't prove it, but it appears to have all the correct parts, clean sharp stock cartouches and no evidence of having been issued.
It is very difficult to do justice to the wood with my camera, but there are very few marks on it and it is in excellent condition. As I said, I can't say for sure that it was never issued, but I'm pretty certain that it never saw combat.
As far as I can tell from the OP's pictures, and it is difficult, it appears that the 03A3 that he is considering might be in similar condition to mine.