I actually now agree with them. I think they were simply doing a bad job explaining.

What I think they mean is that the iPhone camera app is the only one that takes an HDR photo of a scene a produces and HDR output image[0] that can be easily shared and viewed IN HDR on multiple devices.

I don't think that EXR is a particularly portable format (do phones even support viewing them in their native photo viewer/manager?) nor one with small file sizes.

The DNGs from Capture One or Lightroom have similar issues, they at least can be viewed on phones, but they do not show up as HDR images.

Other applications, e.g. Hugin, will produce and SDR image. It's based on an HDR image so it captures a wider dynamic range, but it does it through tone mapping back into a SDR image, rather than actually saving and showing the full dynamic range of the HDR image.

[0] I am not convinced that what the iPhone does with their heic images is really HDR, in the sense that the colors still seem to be stored in an SDR range.