It *is* an actual injury. Your brain suffers physical symptoms as a result.
But differentiating PTSD from other mental health conditions and calling PTSD a "mental injury" would suggest that other mental health conditions are not the result of an "injury", or that the brain hasn't been "injured"..?
But the reality is, for many of the psychotic, mood, anxiety and personality conditions identified by the DSM, we are often, at best, only guessing at the cause. Those conditions might be genetic, the result of upbringing, brought about by drugs, medication or other illness, brought about by trauma, or just be the result of bad luck. We don't really know. But we do seem to be slowly starting to recognise that external factors can change the brain (or "injure" the brain) and mental health of a person, and lead to a variety of different mental illnesses, not just PTSD.
Certainly based on my experience with brain injury patients, PTSD has way more in common with the term "mental illness" than "brain injury", so I struggle to follow the argument that the brain has been "injured"...
Sometimes we change the name of illnesses when we start to under them better, but we don't seem to understand PTSD all that well yet, let alone whether it is innately different from other forms of mental illness. We seem to be able to identify ways that the brain adapts to cope with chronic trauma, but that's not really an injury so much as the brain 'adapting', which is really pretty clever. And neuroplasticity doesn't seem to be far off showing us that the brain can adapt right back again once the trauma is over.
Personally, I don't see what a new label would achieve, other than to make PTSD seem like something "different" to other forms of mental illness, which at best seems to misunderstand (and if not unfairly stigmatise) other forms of mental illness and what causes them.
PTSD is not the only mental illness that can be caused by an external event, nor is it the only condition where there can be changes to the brain from that external event.
My experience of PTSD, for what it's worth, is very much like I have an illness and, more particularly, a mental illness to the extent that that term is used, particularly in its social context.