I don't think this is correct.
According to my understanding of NFL tiebreaker rules, record against common opponents is considered before conference record. Consequently, the Cowboys wouldn't necessarily win the division if they only beat the Giants and Bucs, and then lost their last two.
If the Cowboys beat only the Giants and Bucs while the Giants went 3-0 in their last 3 games, the Giants would win the NFC East by virtue of having beaten the Jets -- a common opponent to whom the Cowboys lost.
Arizona was a common opponent as well, and the Giants beat Arizona. This is why the loss against Arizona wasn't "meaningless." It was actually quite important in terms of determining the NFC East champion.