I don't think it's useful to conflate "programmers and non-programmers think differently" with "non-programmers are unable to think like programmers".
I'd say there are people better-disposed to learning to be a programmer[1] but practice also plays a big part. The end-result is that for a given individual, actually occurring situation, it is a reasonable generalization to say that the programmer and non- do think differently about it at this moment in time.
[1] That is to say, a special type of problem-solver. The individual skills or dispositions aren't unique to programmers but the combination thereof probably is.
It'd be interesting to compare actual neural activity of people in different professions who have been doing what they've been doing for a couple decades. I think that once a person approaches problems a certain way for an extremely long time, that becomes their default -- it'd be interesting to compare a theoretical physicist, a musician, a programmer, a writer, and a doctor (or something along those lines) when they solve different simple problems.
I'd say there are people better-disposed to learning to be a programmer[1] but practice also plays a big part. The end-result is that for a given individual, actually occurring situation, it is a reasonable generalization to say that the programmer and non- do think differently about it at this moment in time.
[1] That is to say, a special type of problem-solver. The individual skills or dispositions aren't unique to programmers but the combination thereof probably is.