Here's one correction I would make to the video in the article about airplane mode:

You don't need to put it into airplane mode, but instead you need to turn off cellular data. Cellular data is the biggest culprit for data exchange with the tower. If you just turn off cellular data, then the phone will still be able to receive calls, but it will only talk a fraction of the time with the cell tower.

Once cellular data is off, the phone only talks with the tower every few minutes in order to update its base station selection. But if cellular data is on, then all your Facebook, Twitter, Instagram or similar apps all talk constantly with the network, and this creates a lot of wireless traffic. Once cellular data is off, this chatter will go to zero, and the only traffic will be base station updates and incoming or outgoing calls.

So if you want a safe(er) phone, but still be able to receive calls, just turn off cellular data. No need to put it in airplane mode.