People need to understand that Schefter has never been a talent evaluator, or a football expert. He's simply a reporter, who gets contract info early because he works for the league. Honestly, I can't understand why the NFL Network even started using him in a larger role, because it's obvious he really doesn't know football all that well.
Getting to what you seem to think Schefter might be hinting to (off the field issues). In another post, I've linked to a Q&A with groves where he talks about his "character issues", and claims the only problems he's ever had were an argument with his wife (not an assault, but an argument that got loud), he stole something when he was ten years old, and got into an accident without proper insurance. During his interview he said that he wanted to be open with NFL teams, and told them everything.
You think he has a questionable work ethic? Honestly, I have to second guess anyone who truly believes this. The guy was a team captain at Auburn, graduated early, came back for his senior year when he could have gone pro, and played through injuries that were especially painful for him in 2007. Heck, he was even happy to switch over to some 34 packages and play LB his senior year, saying he thanked the coaches for putting the packages in. That doesn't sound like a player with a particularly pore work ethic, or commitment to the team.
I have no idea where he'll actually go in the draft, because I don't know if some teams are worried about his surgery, and how that will effect his stock, but on the field (and during draft season workouts) Groves was among the best.