I don't believe anyone other than the airline and/or the visa company are going to be able to give you a definitive answer (and they most likely won't actually do that, even if they can), however if I had to guess here's what I'd say happened...
First, lets cover a few facts :
You obtained your ETA via a third party, and not via the Australian Government directly as is normally recommended. In and of itself doing this isn't a problem, and there are many parties that can obtain ETA's on your behalf, including some that are (in some sense of the word or other) scams, but also many that are not.
The company mentioned in your email, "IVisa Services" from North Sydney was a valid business name, however their business registration was canceled in 2016. This could potentially be a sign of a scam, however in this case I don't necessarily believe it is.
ETA's are normally processed and approved instantly, however around 10% of them will take longer to be approved, generally after they are manually processed by a human. This can take anywhere from minutes to hours (or in the worst case, days). Even then, this presumes that the company you obtained the ETA though submitted it to the Australian Government immediately, which it's possible they did not.
ETA's are generally verified automatically by the airline systems. In the event that the validation fails the airline staff have a number they can contact to verify the reason for the failure and potentially receive approval to board the passenger if there has been an error.
Now, putting all of that together I can see two possible reasons you were refused boarding :
Your ETA had not been processed at the time you attempted to board the plane, but was only approved sometime afterwards. This would explain why you can see it as being valid now, but the airline couldn't. Your email confirmation does say that it's already been approved, but given that this is an email from an unofficial source we can't be certain that it's reliable. It's possible that this company will always claim that it's been approved once it's been submitted, even if it hasn't been.
The airlines validation of your ETA failed for some reason (eg, computer error), and they failed to follow the manual process to confirm you had a valid ETA.