LP needs to eat his own Stetson - to keep his big mouth occupied. Is there anything he's said yet that's been right? He knows no more about Caylee's paternity than anyone else does. I abhor the way he makes stuff up just to keep his lying face on TV.
While there's no doubt LP referred openly that he himself is a media 'ho, I think I have to remove him as the person saying it and look at some other factors which might (and it pains me to say this) make such a statement plausible or even true. The grandparents have their own attorney and the brother, interestingly enough, does not have one. NeJame is only representing the grandparents - why wouldn't he have been made a full family attorney covering the brother too? Why?
I gotta mention that even after hearing this early on in the investigation, sometimes targeted at the grandfather and others at the brother as Caylee's father, I became exteremely annoyed people would speculate about such a thing. Now I am not so sure there couldn't be a bit a truth in it about the brother. The situation, as distasteful as most people (including myself) find it, is a reality in some parts of our society, something people don't want to discuss. It's just a plain fact that some families have secrets about their own family's dysfunction.
IMO, whether you like LP or not, he has had some information earlier than everyone else. Whether people like this particular message coming from him, I found that it raises questions in my pea brain that I'm sure others have already posted, like could this explain the whole "secrecy" about who Caylee's father is, and why the brother has such a different relationship with his sister than the parents do. I have to ponder why after Grund's DNA ruled him out as the daddy that the grandparents wouldn't pressure Casey to reveal the father of the child if only for the child support money -- look how freaky the grandmother appears to have gotten over the towing charge, if the affidavits from the folks at the wrecking company were any indication. Further LP has been stating this openly, and he's got enough common sense, or people around him who do, not to make a claim that can't be backed up.
LP, IMO, expects this information to come out as fact, which is why I think he's even bothering in the first place.