I just had some time to read through FB and Charlie's family asked people not to share information between the parties. They called it a 'major disagreement' regarding the pages. Sounds like (conjecture on my part) that no one trusted anyone from the other family to be in charge of the .
My opinion (which could be wrong) is that it's less about mistrust, and more about two families stressed over loved ones being missing and then acting based on heightened emotions. Add on to the fact that the families perhaps either were not aware, or did not approve of their lifestyle / relationship choices and you have a recipe for heightened emotions. I have seen many families who refuse to believe their loved one could possible make life decisions that do not match with the families morals / ideals, and then look to blame everyone else rather than accept the truth. Look at how some families react if a member comes out gay, or atheist, or dates someone much different than the family, the same issues occur for people who choose to add a little kink to their life. I know many friends either ostracized from their family for such choices, or the family looks to blame others for influencing their loved one; rather than let adults do what they want and be accepting of that.
The families need to form a united front, because regardless of the situation, if you find one you will most likely find the other and/or have a significant lead there. All of the strangers being asked to help and look, need to see that cohesiveness, otherwise people begin to get suspicious or at the very least, frustrated with the waste of energy.
I think the police releasing some info would go a long way into helping this scenario, specifically the following:
1) The last known cell phone tower pings of both phones.
2) If CDCs car was logged going through any tolls, red light cameras, or other traffic monitoring devices.
3) Requesting ip logs from both FB and other social media sites, and releasing any info that can be released.
Maybe all of this information is known, and not released for good reason. Maybe they haven't requested it because they are looking for signs of foul play first. I don't know.