...an algorithm or data structure operation described as being 'O(n)' could really be 'O(n) + x'
No it should not. (O(N) + x) is O(N). That is how it works, is spoken about... What it means!
It is a very simple minded article, and IMO misleading, but it is better than "(O(N) + x) is bigger than O(N)". In the sense of order analysis, it is not.