You could describe it as a PNG issue, since, as you already noted, the Glare node is correctly producing additive values, and Blender is handling them correctly in an associated-alpha ("premultiplied’) workflow, including showing them correctly in that viewer.
In an associated-alpha system, R, G, and B store one physical quality—the amount of light the pixel adds to the scene—and alpha stores another: the amount of light from behind it the pixel removes from the scene. This allows for the storage of pretty much anything: reflections, lens flares, fire, glows, solid objects… (The one thing they can’t do (by default) is RGB transparency (i.e. stained glass, chromatic aberration), since alpha is only one value and not three, alphaR alphaG alphaB. Although, since EXRs can store any number of arbitrary channels beyond RGBA, that functionality is also just a few clicks away (if you have a way to generate it).)
PNGs, by storing their data unpremultiplied, tie themselves to an unassociated workflow, which is also used in programs like Photoshop, where alpha doesn’t measure a physical property and is instead an arbitrary “transparency” mask. When the data goes into the PNG, it’s unpremultiplied (divided by its alpha), and when a program reads the PNG, it has to premultiply it (multiply it by its alpha), which kills any alpha-0 pixels (and also breaks any areas where the RGB might have been brighter than the alpha, since that will produce an unpremultiplied value greater than 1 and PNG only stores 0-1 values). This is a fundamental characteristic of the image format, it’s just how it’s designed to work. EXR, on the other hand, doesn’t require that division/multiplication step, and simply stores the associated-alpha values it was given, which is why people suggest its use in these cases where additive pixels are involved.
Fundamentally, adding alpha to glows always risks situations like this, but I understand that as long as we live in a world where a lot of the major graphics & design programs still handle alpha badly, we’ll keep getting client requests & constraints like this, so… it is what it is.