Thanks for your follow-up and documentation of your experience. There's nothing like information from an actual experience to help others. I think you did a smart thing, you can't lie on your incoming passenger card so being honest with immigration and having your FBI background check in case you need it is very honest & straightforward and I'm sure the officers appreciated that.
The main issue is that lying on the ETA is grounds for entry refusal. And the ETA application wording does not include the 12 months in it. That's why the most conservative advice is to take the 600 visa for any criminal conviction. However if the ETA confirmation email includes the 12 month wording now, then you can use that if the officers ask you why you said 'no' on the ETA. So, fairly low risk as long as that wording remains in the confirmation.
Another interesting data point is that your ETA went through even though you had a FBI record. So, it's very useful to know that if you say 'no' to the criminal conviction question on a ETA but have an FBI record, it isn't automatically rejected.
I do wish Australia would just use the same wording in every location, it used to say 12 months everywhere, then a few years ago that wording largely disappeared. Last time I checked the official ETA 601 documentation did NOT have the 12 month wording and, at least in theory, that would overrule any FAQ or email confirmation as it is the full detail of the visa. But even if the email confirmation is wrong, I think immigration would give you the benefit of the doubt there if you showed it to them.
This is the wording that was in the ETA 601 documentation. It's pretty clear. You've proven it wrong, obviously, in your case.
If you have had any criminal convictions in any country, you should apply for a
Visitor visa (subclass 600), rather than an ETA. If you arrive on an ETA with criminal convictions, you could be refused entry to Australia.
Unfortunately the official ETA 601 page appears to be down for maintenance at this time so I can't check it. But if this wording still remains, it appears that officer discretion could have put you back on a plane. But the fact that you were honest on your entry card and provided them with full detail of your conviction went a long way towards an easy entry.