I can see the first two things happening - I've personally had Alexa hear something that sounds like "alexa" followed by it trying to do something. But the following 2 spoken announcements followed by misheard but appropriate responses stretches credulity IMO.
I don't discount that it could have been faked... but another article I read said that Amazon engineering had reviewed it (presumably the actual audio, though it did not explicitly say that) and said it was indeed a mistake on their part. Still, seems like SOMEONE would have heard her speaking.
Having said that, I have personally witnessed some very strange things by Alexa. In one case while we were visiting in the kitchen at my parent's house, their Alexa randomly started up:
Alexa: "Got it, I found 3 types of pancakes... [listed three, don't remember which]. Which would you like." [Note, there was absolutely NO mention of pancakes in the conversation]
Son: "None"
Alexa: "Okay, would you like to place the order?"
Son: "No"
Alexa: "Your order has been placed."
It was quite funny and my mom was able to cancel her order via the Amazon app. But that is three "mis-hears" right there and two were absolutely spoken correctly. No idea what she first queued on to ask about ordering pancakes.