Sounds very similar to this story[0][1]. If i recall correctly: Ambitious NY Fed employee claims she was fired because she wouldn't soften language in a report; secretly records meetings that show extreme deference to banks. The This American Life version is really great.
It doesn't need to be impossible. The problem could be designed away: on form submission send an email saying 'looks like you already have an account' or 'welcome... next steps' and just show a 'check your email' message in the browser.
[0]https://www.propublica.org/article/carmen-segarras-secret-re...
[1]http://www.thisamericanlife.org/radio-archives/episode/536/t...