They don't need to send your data if you're not working for a US company, or if you're not a US resident/citizen. That is, sending data to the US is not the default. Also yes, the checkbox wasn't just a single box but an entire page just dedicated to FATCA issues i.e. the banks are doing as much as possible to absolve themselves of any FATCA obligations and document it.

Anything remotely connecting a client to the US is kryptonite to banks.