Yes, part of it is registering vets into the system. The other part is a combination of the enormous number of claims and enormous amount of documentation required.
As a physician, I worked in C&P (compensation and pension) clinics for a number of years at the VA, as a consultant.
The amount of documentation required is astronomical, likely because vets are being compensated for their injuries with taxpayer dollars. Fair enough, but a physician providing these services could find other ways to use their time productively (for themselves).
Then there's the volume. You don't just see vets who have lost an arm or a leg or have suffered traumatic brain or spinal cord injuries. You also see the guys who may have sprained a knee or ankle playing basketball in their free time but while they were officially on duty. Throw that into the mix, and you have too many people to examine so thoroughly. They tried to fix this by contracting with an agency and have vets come into a private medical office instead of doctors going to the VA, my partner did this for a while, but the reimbursement offered for the amount of paperwork required ultimately made it impractical.
To fix it:
1) screen vets better, some are clearly more severely injured than others
2) better compensate providers who see all these vets and complete all the necessary documentation.
The screening part is tricky though, as it can quickly get political.
Another possibility would be to not screen them, provide them with a high level of free care as a reward for their service, and just make the system work efficiently. Whether the government is footing the bill, or an individual is, should make no difference at all to the timeliness or level of care they receive. If the problem is paperwork, that should be targeted first.
There is a lot of medical care available (I think "stay on Tricare", etc.) with less hassle. Most of the disability claims are for ongoing cash payments to replace job income, which is more at risk of fraud (and in some cases genuinely uncertain and requiring investigation).
In part the problem arises from the interface between systems. If you walk into any normal hospital internal medicine floor you'll see about 5 different systems in use, with varying levels of interoperability: the VA, operating what is the largest network of healthcare centers in the country, takes that issue to the next order of magnitude. A lot of paper gets generated at these interfaces. Although the core VA EMR system is solid, there are multiple other systems laid atop it. The VA is attempting to address both the software and processes issue (people outside healthcare don't know this, but the VA is the place to take your career if you wish to do healthcare services research - they're, collectively, the single most innovative group of providers in the country).
The main problem lies with the paper backlog of attempting to get people into the system. I'm personally not aware of how/why military personnel's medical records don't transition directly into the VA, but what happens in practice is a gap between military med. and the VA, where vets find themselves forced to file claims. I suspect that this is in large part because the set of "Vets" and the set of people qualifying for VA care, while overlapping, are not the same (that assertion comes from anecdote: I had an ex in the military, and when she finished her tours I recall that she was not qualifying for VA care because she hadn't been disabled nor gone career, as she explained it). While it's fair to ask why this process is done on paper, it's worth-while to note that prior to just the last handful of years the portion of health records that had been digitized was nearly nil (up until about 5 years ago it was standard practice in most hospitals and private clinics to go digital-to-paper-to-digital). Essentially everyone's records were on paper, and all record transfers happened via fax (and still do, if a receiving physician is not inside the same hospital system on the same EMR as the referring physician).
source: work in hospital QI. I haven't worked in the VA, personally, so I am relating a lot of stuff second-hand, but the boundary between most hospitals' QI staff, the IHI, and the VA tends to be pretty porous, if you're in a healthcare capitol city - so I've heard a lot about the VA from co-workers that have worked there, or are currently engaged in ops research there.
The problem is on the medical records DOD uses AHLTA and the quality of records in AHLTA is highly variable. They focus much more on proving immediate care vs. great quality records, both due to the environment where a lot of the care happens and because they're not billing for it.
There are also about 5 levels of bureaucracy to manage a single system within DOD. VA is amazing in comparison (it was really telling talking to doctors who had civilian jobs in the VA but were military reservists and working temporarily in military hospitals...)
Medical records aren't sufficient to make a determination of disability, though, which is mainly what this is about. Having the medical records helps, having personnel records helps.
Another problem is the VA for a long time was focused on long-term care for WW2/Korea elderly vets, and various mentally/physically disabled Vietnam vets. The population of seriously injured younger vets (who could still work, and have long and otherwise productive lives ahead of them, but need specific disability care) is a pretty new thing. That, and the huge number of PTSD/TBI/psych issues.
I'm going to guess that they're two separate things.
Medical records keeps track of medical procedure, patient history, what medications they're on, etc. In the private sphere, this is what a hospital would use.
What's probably at cause for the huge backlog is actually getting people into the system and approved for care. In the private sphere, this is what an insurance company would use.
Or this could be just your standard set of political exaggerations.
The problem with vets is not the absence of software. I am rather tired of seeing this particular horse beaten.