Hello Brooks,
The initial deal refers to: The first two down cards in hold'em...The first four down cards in Omaha...The first three cards in stud, two down and one up...or, as you said the initial pitched cards.
You are correct about "old rules" that did not specify initial deal. As far as the TDA, I looked back and discovered the words "initial deal" were added in 2013. Somehow that slight change was not highlighted in red, as usual, when showing the changes from the previous Summit (2011).
It should bring up some interesting debate. My guess is, multiple boxed cards that occur late in a hand, might conflict with other TDA rules...such as Substantial Action. Look to TDA #34 D) Once substantial action occurs a misdeal can not be declared; the hand must proceed.