By no means am I saying that LSU does not have student athletes that are clearly poor students; I'm sure there are more than a few that fit the criteria you're discussing. That being said, LSU does seem to fare well compared to most of the conference with regards to graduation rates.
For 2011 and 2012, LSU was 2nd only to Vanderbilt in the graduation rates... and there's no shame in finishing 2nd to Vanderbilt in this regard. LINK
I'm not looking very hard, but don't see that they're still 2nd place in 2013 (not sure if the numbers aren't available yet or if LSU dropped... if they did drop it's probably all the early departures to the NFL.
). But I did see this article, saying graduation rates are continuing to climb: LINK
Again, not saying LSU doesn't have some poor student athletes that have trouble staying eligible or wouldn't be eligible without all of the academic assistance available to them, but at least it seems LSU does make an effort to help ensure the academic success of their athletes. What these stats mean in the greater scheme is debatable, but it's a pleasant bit of news in any case.