[bigpooch]

This is absolutely correct. According to theory, you need
to sometimes value bet AA in this spot. For example, if you
consider the models in "The Mathematics of Poker", by Chen
and Ankenman, in this situation (big blind versus button),
when both players have drawn three, the distribution of the
hands are very close and so can be approximated by the [0,1]
toy games discussed in the book.

You wouldn't be far wrong to value bet AAK and AAQ from the
button and you will have to sometimes bluff with 99 or 88 if
you are playing "well".

The TMOP models are useful not only in this spot, but also
in two other scenarios (both only two players left in the
pot):

1) capped pot with two pat hands
2) capped pot in blind versus button/aggressive cutoff where
both players have drawn two to trips

In these scenarios, the toy games in TMOP can be used to
approximate optimal play.

Big blind bets
--------------
If the big blind bets, you need to call almost routinely
with AA on the button because if you don't call with AA,
what will you call with? If you don't at least call with a
frequency of 9/13 in this spot from the button, the big
blind can play exploitively by bluffing with a frequency
greater than that of the game theoretical bluffing frequency
and thus profit from the insufficient calling frequency.

Assuming the button will open with 99A or better and calls
in accordance to game theory, and draws three to all pairs,
if you are calling with the top 0.568 of unimproved pairs,
this translates to KK and almost any pair of queens. Of
course, in practice, the big blind may not be bluffing often
but against a big blind that bluffs close to optimally (or
even a bit more!), you need to call with QQXxy or better or
you will simply get "run over".