I trust my browser's developers with my most sensitive data (online banking password, government id etc.) but that does not mean I believe I am fully secure in doing so. There could always be a bug in the WebRTC implementation or the SSL library or the hardware. Maybe I should rephrase the FAQ to read "Don't put your highly sensitive data on the Internet at all".

The warning is posted under the headline "How do I know you're not sending my data to the NSA" and in that context, it is a good warning. Don't trust random software with highly sensitive data.