However, if the people holding the cellphones are near the camera shooting and hillary is across the room from that (long lense) camera , how can both be in focus? Shouldnt the people and their phones be so out of focus we wouldnt be able to make out whats on their screen? Isnt that depth-of-field?

Try an experiment some time. Close one eye and look at your finger right in front of your eye, then look at a distant tree or mountain or building. You can see/feel your eye refocus (people with certain eye lens replacement surguries can't do this though). Now look at a distant tree or mountain and at the moon at the same time. They can both be in focus. Even though the moon is a million times farther away than your finger is from a tree. You can also see this in photographs, an entire city skyline can be in focus while an object right in front of you might not be. Sometimes things far enough away don't need the level of precise focus they need up close.

Not to mention, depth of field changes dramatically based on the size of the camera sensor and on the F-stop. A really high f-stop has a much longer depth of field than a really low one is. So if there's enough light in the room or a really fast lens, then it's not hard to get good focus on a number of distant subjects.

For a good example, consider some of those film clips, like the one from tinker tailor soldier spy, where the plane is in focus at the end, but is probably still very far from the actors.