"All vets are mentally ill" is not close to the same as "find a way that veterans who are incapacitated for one reason or another mentally don’t have access to this kind of weapon."
I would say her real statement is stupid for two reasons. One, PTSD is a product of any violent situation. It's not a product of just the Iraq War. Two, she should be talking about how to identify any person with mental issues rather than just veterans. That is what really got the negative attention.
Mentally ill people for the most part are largely non-violent. Most violence in this country is done by people who have been drinking.... Alcohol use is probably a better predictor of violence than mental illness. The people who do these shootings tend to be young males, and some of them are psychotic, but not all of them. Some people with psychosis are veterans, so at best veteran status could only be viewed as a flag on someone's history when looking for potential spree killers. The most common factor for this kind of crime is gender: males, and age.
The problem with our system is not really IMO the guns, but preventing access to them by people that are known to be unstable. In most of these mass shootings, the unstable behavior was noted for years. But if you are a friend or relative of a person like this, you know that there really is nothing much you can do about them. Your friend/family member cannot be forcibly committed except in extreme cases, there are almost no long term treatment facilities for them to go to, except prison. If you know someone who is elderly and shouldn't be driving, you can drop a card at the DMV with their name, and they get called in for a drivers test/evaluation, but if you know someone who has the potential to act out violently with a gun, there really is no one you can call for preventative help.