I don't believe that's quite correct. I was told that if the person does get that next concussion, he/she is more prone to that next concussion being a 'more severe one', than if they never had one prior.
This proved absolutely true in our case. I have a family member who had two concussions over the course of 12 months, and while the first concussion was a result of a nasty blow to the head, the second one (a year later) was a fairly mild, innocuous hit to the head. I was there and saw both of them live, and couldn't believe that she was so hurt from such a mild blow that second time. However, that second concussion was far, far, far incredibly worse than the first one. The effects lasted for months.
So that person went to the concussion specialists in Golden (we were told by multiple doctors/trainers that these are the best concussion docs in Colorado), and they told us exactly this: Subsequent concussions can get worse and worse, even if the blow to the head isn't as severe as the first time. We were also told that concussions often are absolutely cumulative, not individual events, even if they happen after complete recovery. These are not my words - they come from the doctors at the REAP Concussion Management Program at Rocky Mountain Hospital for Children.