Just want to point out that any company can use the word "HEPA" as there is really no industry standard/federal minimum for what it means to be HEPA. So you can basically have a paper towel in the back of a fan and call it a HEPA filter.
[0] E.G., http://energy.gov/sites/prod/files/2013/06/f1/doe-std-3020-2... and https://en.wikipedia.org/wiki/HEPA#Specifications
You are mostly correct. However, per your links, using "HEPA" with any prefix or suffix is problematically allowed. The specifications laid out by the DOE are mostly for DOE facilities and so they have their own version. Everyone else is using their own brand of "-HEPA-" which can mean <0.003 pm or not and is therefore misleading.