From a strictly theoretical point of view, some incorrect notation can result as a consequence of this simplification. For example, if you display an A major scale with display = ♭, you see D♭, G♭, and A♭ instead of the correct C♯, F♯, and G♯.
However, from a practical point of view, the notes are correct.
As a beginner, I spent hours on the internet searching for clear information about violin positions. I could not find one source giving coherent information, but found several sites with fuzzy and unclear information. The most common are: "finger replacing finger", but fingers have several possible positions (low, up, normal, extended, …) for each violin position, and "natural note replacing natural note", but they do not fall identically on every string. I also found some contradictory information between different sources, even about the very common third position.
I guess it is an "experience makes things obvious but there is no math for it" case. So I chose the following simple convention: 1 position = 1 tone (= 2 half-tones). It may not be true for every experienced violinist, but it is simple, clear, and it seems to match most of the definitions I have found for each position.