That's the red dot's selling point but, sorry to say, it just isn't so in real application.
Red dot sights are made with an offset illumination source and, therefore, are subject to POA shifts due to parallax.
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ALL red dot/holographic sights exhibit parallax to some extent. It's minimal with some makes and horrid with others. The Fastfire has more than most.
Here the parallax of some different red dot sights is compared. Red dot sight POA shift due to parallax is incontrovertible.
The closer the sight is to the eye, the greater the apparent shift. That is why I saw so much POA shift when I mounted the Fastfire 3 on the rear of my Garand receiver, just in front of my eye. It was horrid! However, I experimented with the sight and found that when held 14" from my eye, about where it would be on my pistol, the shift was almost imperceptible.