Nick: In my opinion, I don't think you've been doing it wrong, and I also don't think that diz is doing it wrong either. Earlier in this thread, Brian probably made the point the best: that there is a "classic" way of doing it, and the "progressive" way of doing it. You and I are probably more accustomed to seeing it done the "classic" way, and diz is arguing for the "progressive" way.
I think that confusion arises because there's been a mish-mash of rules from different rule sets that TDs have tried to apply over time to the 'challenge' of balancing tables. To make the problem worse, we probably worked through the period where the popular method for button movement evolved from "moving button" to "dead button", but no one bothered to explicitly define how the act of balancing tables should differ depending on which button movement was being used.
In this example, diz can justify seating the new player in seat 6 with the BB, and placing the button in seat 5, because he relies on a part of the current TDA rule that says that the player should be seated in the "worst position" and that the same seat can "take the big blind twice". This is justifiable, but in doing so, he has to ignore the next part of the rule that says "Worst position is never the small blind". Note that if the button is in seat 5 and the new player is in neighboring seat 6 as the new BB, he is effectively requiring a "dead small". But note: there is no seat reserved for the small blind in the "progressive" approach. This is NOT the classic "one big blind only case" where the previous BB busted leaving the seat for the player that ought to have been the SB next vacant. It is arguable whether it has ever been acceptable to have a "one big blind" scenario where there is not even a vacated seat designated for the "dead" small blind.
To make things even more complicated, Robert's Rules states that in a tournament, "new players to a table as a result of balancing tables are dealt in immediately unless they are in the small blind or button position, where they must wait until the button has passed to the player on their left". If you can balance a table by eliminating the small blind's seat at the new table altogether, then what would be the point of this rule? What's the point of saying "worst position is never the small blind" in the TDA rule if you can always simply eliminate the small blind's seat altogether?
Here's another take on the same situation. If Seat 5 is vacant and destined to be a "dead" button and seat 6 is vacant, and diz says that the new player should be placed in seat 6 because it is the worst position, why stop there? Why not simply put the new player in seat 5, have the new player post a BB, and move the button back to seat 4? If one is OK with eliminating the SB's seat altogether, then why move the button at all? We don't do this because most people expect the button to move at least one position. In the same way, I think most people expect that there should also be a seat reserved for the small blind, even if a small blind is not actually posted because the seat was recently vacated.
Confused? Me too. All I am saying, it is too simple to say that either the progressive way or the classic way is "clearly" suggested by the current rules. It is not clear. Some will argue that the "classic" method fails to put new players in the "worse" position possible, while others will argue that the "progressive" way requires eliminating a seat to be assigned to the small blind which is not justified anywhere in the rules. I agree with you Nick that there are various solutions that could work, possibly better, and at least both ways are probably justifiable.