HDR is a method for accurately displaying real world lighting.
HDR essentially allows you to have a much finer graduation between the light and dark parts of an image, resulting in a more realistic scene.
It makes effects like bloom and reflections look better as a result. It's got nothing directly to do with bloom. It's really just simulating the real-world potential of the human eye, not just an effect.
You can have bloom on a non-hdr image, it just won't look as good.
So, it is perfectly reasonable to say it's just better.