My bet would be that this is down to data quality, and other influence which overrides the forces part. I've no proof of this (other than experience), but my bet would be if you compared the qualifications of those prior to going in the forces, with others of a similar level in/ out, then homelessness would be quite close.
I still think forces homeless might be more but I bet it would narrow the gap right down, and I'll eat my hat if it's not because more people get institutionalised into a simple life with little self control/ responsibility, rather than making out that everyone's got PTSD or had major injuries/ medical discharge long before their pension starts paying out.
People in the forces largely don't have the drugs excuse either, as everyone is getting drug tested often, it's basically protecting you from a massive hole which is open to others. Same with healthcare and dental etc, nobody in the forces is waiting more than a day for an appointment, I'll bet you that. Same with surgeries or treatments which are stopping them from working (which can be treated).
There's another side too, which doesn't get talked about anywhere near as much. The forces gave so many people good, free education with zero debt (like how I benefited) and there are so, so many people who abused that to move from a 25k job to a 50k a year job, and then a 100k a year job. I even know a few on over 200k, and loads of those are tax free too! I can't think of any forces guy who left around the same time as me, from a similar job as me, who now isn't earning at least double the pay they were getting in the forces and double the national average wage, and that's in places which are not well off at all.