I don't think there's any debate about what a TAA is.
@MauleSkinner already quoted text from the AIM stating that once you're cleared for an approach, you can descend to TAA by default
unless ATC gives you an altitude restriction. Any altitude restriction would override the TAA. What we're discussing is the limit of the altitude restriction that the OP received "until established". If "until established" means "until you're on a published segment of the approach" (as the controller glossary suggests), then the altitude restriction the OP received is in force until the OP is actually on the approach, probably via a waypoint that they were cleared to directly.
This is exactly how an MSA works in Canada. By default, an approach clearance means that you can descend to MSA
unless ATC gives you an altitude restriction.
Here's a non-RNAV example. If ATC says "
Fly heading 100 to intercept, cleared for the ILS 07" then I can descend to MSA (in Canada) right away; however, if they say "Fly heading 100 to intercept, cleared for the ILS 07, maintain 3,000 until established" then I can't descend below 3,000 ft until I'm established on the localiser track.
In an RNAV case, it would be clearer to say " Maintain 3,000 until XXXXX" where XXXXX is the initial waypoint you're using to enter the approach, but if they said "Maintain 3,000 until established", I'd still assume they meant that.