Assuming all other factors are constant — a drop of conversion rates by 70% implies that real users are also getting tripped up with AMP.
Even the author couldn't narrow down what exactly was the cause other than maybe:
a) the domain name being different
b) the addition of chrome w/ a link to Google support + a notification "You're now logged in as [user]@gmail.com"
c) minor CSS changes as a result of minimizing static assets
None of these screams an obvious problem, especially given the other benefits this process has given in return (which of course could be accomplished without AMP).