If perfect knowledge is the standard for interpreting historical events, then little history can be written. Eyewitness testimony can be dubious and even contemporaneous documents cannot cover quirky circumstances. What are we left with then? Only reasonable inferences drawn from available sources - and an honest discussion of their strengths, weaknesses, and ambiguities. While skepticism is good and can lead to a better answer, it's difficult to convince someone who requires perfect proof.
The case for the 1917 has good circumstantial evidence to support it, but with no direct participant account. Nothing in this case precludes the use of the 1903. The 1903 case has a secondary source that speaks directly to the issue (something the 1917 case lacks). As John explained, the secondary source was probed for believeability and found solid: no evident bias on the son's part; access to the participant; adequate knowledge of the subject; a clearly recalled discussion directly addressing the issue at hand. The only argument against this account is that Alvin York had a faulty memory with the passage of time or had a bias himself. On the movie set, isn't is reasonable to think that after the Lugar swap for the 1911 had to be made that York would have been especially tuned in to the shoulder arm question?
In my mind a solid secondary source is better than relying on general principles like what the unit was issued.