This claim is so absurdly easy to verify with that 3rd party that I'm actually decently sure this isn't corporate espionage.
In a suit, at least, they can compel discovery and demand accurate testimony.
"Ya know that uber design which is the same as ours? Mind accidentally CC'ing johnsmith@google.com instead of johnsmith@uber.com? Since johnsmith used to work for google, it would be an honest mistake, and would give us the evidence we need to take this to court"
You can't act as they have and not have hordes of enemies!