Steven:
In order to answer your question, I want to explain what I believe the TDA is addressing. Player A bets 100, Player B Raises 170 more (total 270). In order to evaluate the size of the raise, some dealers will size the bet against the raise leaving only the raise amount in the betting area (not in the center pot). This will make the size of the raise "stand alone."
The practice is not approved by the TDA. I must confess that I am guilty of "bringing in chips" especially when dealing no limit, and when action is head to head.
Bringing in bets, does not require a count, or any further breakdown of the stack. It just makes the amount required to call easier to read. IMO