First, the image of severe brain damage doesn't apply to every case. According to the Mayo Clinic,It sounds like what used to be called a concussion, and that there's a wide variation in the severity of injury.
Traumatic brain injury is usually the result of a sudden, violent blow to the head — which launches the brain on a collision course with the inside of the skull. This collision can bruise the brain, tear nerve fibers and cause bleeding.
Traumatic brain injury may also be caused by objects such as bullets or even a shattered piece of the skull entering brain tissue.
The severity of traumatic brain injury can vary greatly, depending on the part of the brain affected and the extent of the damage. A mild traumatic brain injury may cause temporary confusion and headache, but a serious one can be fatal.
Now, where does the one-in-five figure come from?
An article in the New England Journal of Medicine(1) reports,
According to the Joint Theater Trauma Registry, compiled by the U.S. Army Institute of Surgical Research, 22 percent of the wounded soldiers from these conflicts [in Iraq and Afghanistan] who have passed through the military's Landstuhl Regional Medical Center in Germany had injuries to the head, face, or neck. This percentage can serve as a rough estimate of the fraction who have TBI, according to Deborah L. Warden, a neurologist and psychiatrist at Walter Reed Army Medical Center who is the national director of the Defense and Veterans Brain Injury Center (DVBIC). Warden said the true proportion is probably higher, since some cases of closed brain injury are not diagnosed promptly. (emphasis mine)
In 2006, another group of doctors did an "anonymous survey of 2714 soldiers from two U.S. Army combat infantry brigades — one Active Component and one Reserve Component (Army National Guard) — 3 to 4 months after their return from a yearlong deployment in Iraq. The units saw high levels of combat, similar to those of other infantry units." Of those who responded, 15% had suffered injuries and symptoms defined as "mild traumatic brain injury."(2) (The survey didn't seem to be looking at those who had more severe brain injuries.) What did they consider a mild brain injury?
A soldier was considered to have had a mild traumatic brain injury if any of three questions — regarding “losing consciousness (knocked out),” “being dazed, confused, or `seeing stars,'” or “not remembering the injury” — elicited a positive response.
This raises the question, What portion of troops in Iraq and Afghanistan are combat infantry? An article in the New York Times(3) reads, "According to Pentagon statistics, about 23 percent of the troops currently assigned to the Iraq mission conduct primarily combat jobs."
In other words, perhaps 15% of combat infantrymen serving in Iraq and Afghanistan sustain mild brain injuries (probably, fewer of them sustain more serious brain injuries) and around 22% of badly wounded troops have traumatic brain injuries.
If we assume that non-combat troops are a lot less likely to be wounded, and that most troops aren't wounded at all, and that many troops are assigned to places other than Iraq and Afghanistan, the one-in-five vets having traumatic brain injuries sounds unrealistically high.
(1) "Traumatic Brain Injury in the War Zone," New England Journal of Medicine, May 19, 2005
(2) "Mild Traumatic Brain Injury in U.S. Soldiers Returning from Iraq" by Charles W. Hoge, M.D., Dennis McGurk, Ph.D., Jeffrey L. Thomas, Ph.D., Anthony L. Cox, M.S.W., Charles C. Engel, M.D., M.P.H., and Carl A. Castro, Ph.D. New England Journal of Medicine, January 31, 2008
(3) Pulling Out Combat Troops Would Still Leave Most Forces in Iraq by By THOM SHANKER, New York Times, Published: December 10, 2006.