In the past (some years ago) a popular thing around these parts was the so-called Lazy Man's TEK, ie. a straight-to-base, easy MHRB TEK. Successful yields made easy, proven track record.

Lately I've seen "new" TEK's with basically the same process as in e.g. the Lazy Man's, but with an extra step at the early phase of the TEK including vinegar.

Can someone possibly shed some light on why this is (supposedly) beneficial? Thanks!

Its not new by any means. Extracts into water away from the plant material making a cleaner solution that can be reduced to a smaller volume. Saves mess and solvent and is neater to work with. Called an A/ B check the wiki for more info.

I'm not certain if it has been proven without a doubt, but my understanding is that A/B often produces a higher yield as well.

EDIT: I think maybe the heat that is typically used in conjunction with the acidic soaks might help to break down the cell walls, releasing more of the plant's alkaloids into the solution. Adding just enough water to wet the plant matter thoroughly and then freezing and thawing a couple of times can also help to lyse the cell walls.