There has long been talk on public forums about whether the A family members ought to be/will be charged with any criminal wrongdoing, and LE has long denied that they have any current plans to charge them. IF they do, they aren't saying. Maybe LE doesn't know yet. Maybe they don't want to ever, as they are kinder to the family than the family is to them.
Against this backdrop, the new attorneys for all of them have sought out public forums (like appearances on national tv, press conferences, etc.) in which to raise, at the first opportunity, the immunity issue about their own clients. I don't know their motivations to a certainty, but if there is increased speculation about possible charges, they have only themselves to thank for it. From the GP's attorney, it almost seemed an admission of some lesser wrong (making some inconsistent statements), which they supposedly would not repeat, and a suggestion they would be all cooperative and whatever in exchange for immunity in the future. Not the best PR, as it reinforces the idea that they tend not to tell the truth as a default response and just won't do the right thing ever just for the sake of doing it. In the case of LA, it was more like whining from his attorney and spin: LA just carried on his own investigation and is likely to be charged, but wrongfully so.
Assuming for the sake of argument that these new attorneys are not bumbling fools, I'd guess this is all part of the new overall defense plan that was rolling out just before Caylee's remains were found. There must be a plan to gain something here, on behalf of the clients AND Casey's defense, which her family members undeniably promote. What?
I don't know how serious, but they all SEEM to have some worries about potential charges. So, for example, why wait until trial, get called as a witness, invoke your right not to self-incriminate, get immunity shoved on you and be forced to testify without full preparation time or go to jail for contempt. Why not know what is coming, explore NOW what they might have or think they have against you, have time to prepare, get insight into the case against Casey, know for sure whether you are going to be able to retain and sell your story about the case, avoid any perjury possibilities for coming clean only "part way" when LE knows "all", etc. etc. I just don't believe as a rule that lawyers act to the detriment of their clients for just no reason. There has to be something in it for the clients. Either immunity they need or something else (like my what if, above). The discovery of Caylee's remains and the house searches that followed seem to have evoked a response from the A's/their attorneys. They know every single item that was seized and they have the information to put them in context. And this is what they have said. We'll see.