When back-pedaling from blaming violence on mental illness, it is common to divide and conquer. "Oh, no, I didn't mean all people with mental illness, just people with ____" (Usually the blank is filled with schizophrenia and/or bipolar. But I've also seen other diagnoses, including PTSD, come up in these kinds of discussions.)
This is also not okay. Narrowing the group of people against whom you are stereotyping does not make the words any less discriminatory.