Google and Amazon are huge companies and would face serious liability for falsely advertising that their devices only listened upon hearing the wake word. Moreover, I'm sure someone out there would analyze the network traffic and figure out it did not work as claimed. They have nothing to gain by secretly transmitting data, and everything to lose.
State adversaries are a different story. I don't doubt the NSA might somehow break into Snowden's Echo, but most people don't have such adversaries.