Do you mean thin crown or crown guard?
As for the crown itself being too thin, some models have really thick crowns and the rep manufacturers tend to use the same ones all over. This creates a problem with a crown being a little too thin on a model that should have a thick crown. Sometimes people go a little overboard with this though. Not every PAM has the uber thick crown that people think they do. Many people just want the crown to be thick because a thin crown can scream fake. The very cheap replica Panerai usually come with crowns so thin that they can cut your finger.
Going by evildee's example, this is what the gen of that model looks like.
As you can see the crown on the rep is not that off from the gen crown. They are both about the same thickness. Some people look at the reps with out paying enough attention to the gen and it can get them in trouble.
Here are some pictures of a gen 111
G series
H series
Here is a picture of a rep (from Joshua's site)
H series
As you can see there is a difference. The gen is thicker than the rep on this model. The best thing to do for crowns, is to take a look at the gen of the watch you are interested in and double check it against a picture of the rep. If there is a huge difference then you may want to stay away.
Now, for thin crown guards..... The only thing that I could guess would be people worried that the crown guard is not as beefy as the gen. To me this is still an issue of the crown more than the crown guard, but I can see the difference.
Gen
Rep