I've heard before that there is an actual distinction between the two. To "agree", as I understand it, is to believe that that a person's decision, opinion, or what have you is correct.
To "concur", on the other hand, would mean that you came to the same opinion/conclusion on your own.
For example, after Susan broke up with me, Dave and Bill independently came to the conclusion that it happened because she walked in on me wearing her underwear. As such, they concurred. On the other hand, although I initially had no idea what drove her to break my heart, once Bill and Dave explained how my actions were not socially acceptable I was inclined to believe their assessment was correct. Hence, I agreed with them.
Does anyone know if this is an actual dictionary difference? Or do "agree" and "concur" legitimately have the same meaning?