Now I'm Confused About the Q3 Auto Production Numbers...

Tim Duy confuses me. He writes:

Economist's View: Tim Duy: Third Quarter GDP, Part II: Third Quarter GDP, Part II, by Tim Duy: A bit of a controversy is simmering with regards to the jump in auto production as reported in 3Q06 GDP report.... I was surprised as well – but I quickly thought to myself “oh, so prices fell.” Didn’t seem like a big deal, so I was caught off guard by the controversy.... Truth be told, the BEA is not helping itself.... [A]s I explain every time I teach principles of macroeconomics, in practice the BEA does not measure output. Instead, the BEA measures demand:

GDP is measured as the sum of personal consumption expenditures, gross private domestic investment (including change in private inventories and before deduction of charges for CFC), net exports of goods and services (exports less imports), and government consumption expenditures and gross investment. GDP excludes intermediate purchases of goods and services by business.

For instance:

Personal consumption expenditures (PCE) (1–15) measures goods and services purchased by U.S. residents. PCE consists mainly of purchases of new goods and of services by individuals from private business.

In the background, the BEA is making use of the “national income equals national output” identity.... The 3Q06 “mismeasurement” of auto production is a perfect example – the supposed automobile “production” component of PCE is a measure of final sales, not production.... In converting from nominal to real, a decline in prices yields a positive increase in real sales, even if nominal sales stay constant (or even fell). As a demand side concept, this is not a problem. If the price of automobiles falls relative to other goods in my basket, I am unambiguously better off as my budget constraint increased. The real quantity of aggregate goods and services I can consume is greater. No mismeasurement. One, however, has to be careful of the supply side interpretations...

Now I am confused. Real GDP is (a) real final demand, plus (b) the change in business inventories. If cars were sold more cheaply in Q3 than anybody expected--and thus if the same flow of money spent on auto purchases resulted in more cars sold--then the extra cars sold must have come out of inventories, right?

Auto companies didn't ramp up production in Q3, did they?