I think you missed the part in the video where the lady, clearly overwhelmed with emotion, states that because of this little girl and her father, she was able to charge her phone and contact her family to let them know she is alright.
Cellphones are quite important, especially in a disaster stricken area where it can be your only form of communication. Yeah yeah, people can survive without a phone. But ya know what, we can survive without toilet paper and clothing. Now let's see a show of hands of people actually willing to forgo those things. Anyone? Anyone? Bueller? Didn't think so.