I'm not sure how accurate this tactical liquidity picture is, at least for much of medallion's history. For a good portion of their existence they called in all their trades twice a day. Them being fairly late to the automated trading game was one of the the surprises from the book for me. Any "HFT" as mentioned in the article is not done by renaissance, but through execution services.
The big picture seems to be statistical arbitrage done with extreme precision and leveraged to a massive scale. Add in some quasi-legal agreements with banks, and likely tax-fraud, they are able to do this at a magnitude no one else can.
Providing liquidity doesn't necessarily mean HFT. It doesn't even necessarily mean classical market making.
Here's how I like to think about liquidity. It's the market's ability to absorb random imbalances in the non-informed order flow (while still correctly engaging in price discovery for informed order flow). In other words it looks a lot like what economists call price elasticity. Having a lot of participants who are very price sensitive makes prices stable by keeping demand responsive to small fluctuations.
On the very short horizon that's done by market makers and HFT participants. They're quoting a tight two-sided market so that as orders arrive the price remains stable. But HFTs keep very small inventories[1]. They're unable to absorb the typical imbalance seen on the scale of hours, or even minutes.
There exists a secondary class of participants, usually grouped under the catchall category of "stat-arb", that exist to fill this need. They're still trading directionally, but that direction is very sensitive to recent price moves on the scale of hours or even minutes. Moreover they tend to overwhelmingly trade in a mean-reverting manner.[2] Effectively these participants "provide liquidity" in the sense that they're stepping in and absorbing imbalances in the natural order flow.
I don't disagree with anything you've written. But if you name a strategy, I can make a case for why it's providing liquidity.
On the one extreme, some firms truly are paid to make liquidity. This is the basis of the maker-taker model. I think Rentech is at the other end of the spectrum.
The big picture seems to be statistical arbitrage done with extreme precision and leveraged to a massive scale. Add in some quasi-legal agreements with banks, and likely tax-fraud, they are able to do this at a magnitude no one else can.