Can you be charged just for leaving your cell phone on?

I’ve never heard of such a fee. Maybe they misunderstood the term “air time”.

It depends if they have things (email, for example) that automatically synch. If so, then every 15–30 minutes their phone will be checking for new email, and if there is some, it will take some bandwidth to download it. Depending on the person’s cell plan, that might cost them money. particularly if they are overseas.

Most people who keep their phones off do so in order that they cannot be tracked.

No, they do not charge you extra… unless you are roaming. However, roaming nowadays no longer means just being in a different town or state like it used to. Most plans these days only charge roaming fees outside of the US.

But even then, it only matters if you actually use the thing. Most smartphones will periodically transfer little blips of data (Facebook updates and such) but an old dumbphone only counts if you are making/receiving a call or sending/receiving text messages.

It sounds to me like either somebody is so technologically inept that I am surprised that they even know how to turn their phone on/off, is still stuck in the ‘90s, or (more likely) they prefer to remain unreachable.

If you have a cellphone that keeps checking data or updates using a data link yes. One of the ways roaming charge in a foreign country can roll up a HUGE bill.