Sorry, but from this description it seems that the gateline staff were doing what the railway asks them to do: no valid ticket, no travel. Not what perhaps what passengers want to hear, but the rule is that you need a ticket, not an email confirmation, to get through the barriers. This is the case anywhere on the network, not just at MIA.
Recall that ADV tickets, like all other types, can be changed right up to departure so there is no certainty that an email confirmation would be for a ticket which is still valid on that departure, ie. it might have been changed. The ticket is the only proof that a valid booking exists. ADV fares offer a discount because they are tied to a particular train. It is the passenger's responsibility to be sure that they can get to the train in time, at the risk of having to pay for a new ticket if they don't. So, really, tickets perhaps need to be bought perhaps a little further in advance than seems to have happened here, or a flexible ticket purchased. Some retailers' apps, of course, won't let pax buy tickets of any type for trains within 15 mins of departure because of the potential delay in sending an e-ticket to head off problems of this kind. This approach could be adopted more widely, but the better approach as per td97 is to use a retailer that can provide instant tickets within the app?