I understand this is not your answer, nut from BARD, but you do seem to accept it as understandable and true. I am afraid I am still in the dark as I will point out below:
How exactly does that work. We have no idea how many shares they hold of a certain Co, Nor do we have any visibility to the internalized short, so how does this "create the illusion that they have more shares available to sell than they actually do"?
"By internalizing their short sales, they can keep their positions hidden." Maybe, but they have also carried the cover for the short as it was internalized, so the two are effectively neutralized and have no real effect on the market,
BARD does not explain just how this price manipulation is accomplished.
The fact that a trade is also part of a block trade doesn't really make a difference to the visibility, as it is already not visible as a part of an internalized trad.
BARD uses a lot of words but doesn't really explain the nitty gritty of how internalization achieves its effect he asserts that it has.