Apple TV 3rd generation
Yes, there is a way out of this conundrum, assuming you have a bluetooth keyboard? It doesn't have to be an Apple bluetooth keyboard, any bluetooth keyboard should work.

Follow these steps:


Disconnect the keyboard from the device it's currently being used with and switch it off
Switch on the Apple TV
Switch on the keyboard
Your Apple TV should recognise the keyboard and prompt you with a code
Enter the code using the keyboard
Once the keyboard is paired, you can use it to navigate through the Settings and add your Apple Remote app
Once connected and everything is okay, switch off your keyboard and reconnect it to its original device


Let me know if you run into any problems.