iPhone not compatible with device - when it's not connected to anything

When travelling, I use my iPhone as my alarm clock. So I put it on Airplane Mode so it doesn't buzz when e-mails or calls come in. Last night, it was on Airplane Mode, wifi was off and so was Bluetooth. It wasn't plugged into anything.

Early this morning, I was half asleep but noticed it got brighter in the room. The phone had lit up. It had an error message: "This device is not compatible with the iPhone" (or some similar). I think that's strange, because the iPhone wasn't connected to anything.

Later on, I turned off Airplane Mode and got ready for work. I got the error message again - but still, it wasn't connected to anything (and still no wifi or Blutooth, both turned off).

It wasn't the normal incompatible error message I've seen when actually connecting the phone to a device, the one that asks if you want to go into Airplane Mode.

Anyone experienced this before? I did a reset once, and it did it one more time (this time with the longer error about switching to Airplane Mode), but hasn't done it since then.