Vet hospital ?
In the US military vets are treated in separate hospitals from everyone else ?
Are they state funded then rather than via medical insurance ?
Since nobody has answered this, I will.
US Veterans receive veteran benefits, including health-care, but in order to use their veterans insurance they must go through a VA(veterans affairs) hospital as seen in this movie, of course in cases of emergency they can goto a normal hospital although will be transferred over to a VA as soon as it's possible and will likely be billed accordingly for their time spent as anyone else would be for having been in the public hospital.
As for their funding, yes they are state funded(US government).