The handbook I'm looking at is
here. Orthodontics is mentioned on Page 9 of that book, so it might be the case that they've updated it since your renewal and only the most recent version is online.
It doesn't matter if that's the case or not though, because the one that's relevant is the one you were sent when you last renewed (or joined if it's still your first year). (the rule book and the handbook are the same thing btw.)
According to what you're saying, your handbook doesn't mention a threshold, so I don't see how Aviva can apply it in your case.
For clarity, ring Aviva again, and tell them you've looked through the handbook and can't find mention of the €4,000 threshold. Ask them where it's referred to in the handbook. If it isn't on the page they refer you to, then tell them so, and ask them how you can identify which version of the handbook you have so that they can look at the same version. The terms and conditions may have changed during the year, but this only applies at renewal, the terms can't change mind policy year, unless it's specifically noted (e.g. hospitals covered, etc).
This may also explain the 10% discount you mentioned, which is mentioned in the book I link to above. Avivia and Smiles may have introduced at the same time as the €4000 threshold to mitigate any adverse reactions.
Hope that helps matters. If Aviva say anything else about the terms and conditons/handbook/rule book, get them to refer you to where it says that in
your handbook, because that is
your most recent contract.