auto-complete defines three keymaps that might be relevant here:
ac-mode-map: This map is active when auto-complete-mode is enabled. ac-set-trigger-key adds the binding for the trigger key to this map.
ac-completing-map: This map is active during completion. By default, TAB is bound to ac-expand in this map.
ac-menu-map: This map is active while the popup showing possible completions is displayed (in addition to ac-completing-map), but only if ac-use-menu-map is set to a non-nil value.
If you want to make sure TAB won't do anything that's even remotely related to completion, you should probably "unset" the bindings in all of these maps (using the same technique you demonstrate for yas-minor-mode-map in your question).
UPDATE:
Here is a minimal configuration that keeps TAB from doing completion:
(package-initialize)
(require 'auto-complete-config)
(ac-config-default)
(define-key ac-mode-map (kbd "TAB") nil)
(define-key ac-completing-map (kbd "TAB") nil)
(define-key ac-completing-map [tab] nil)
You can try it out by starting Emacs via emacs -Q, copying the code into the *scratch* buffer and running M-x eval-buffer RET.