Just to clarify, did the charges show up on your most recent bill or was it just the notification saying you will be charged?

If they have shown up, it may be hard to dispute some of the charges as if you did fly over a country, connected to their network and then used the network, you fit the categories for roaming charges.

Where were you flying from? Going forward, I suggest you turn on airplane mode when flying. This is also instructed by the flight crew before take off and will prevent charges occuring and messing with flight instrumentation.

I just got the notification- I did not access the network in any way and didn't intend to, I simply forgot to hit Airplane Mode. 

In that case you need to wait for the bill to be issued. This is because even if you did connect to the network, you might not actually be charged. The message you received is just an automated one once you connect to a foreign network.

If the fees do show up on the bill, drop a message here again and we can have someone look into things.

I would also considering keeping “data roaming” setting turned off until you need to roam as another step to help prevent unwanted charges. You can control when you make and receive calls, and outgoing SMS, but not really data usage.