I don't think they ever used the term "payment for order flow" but I'm pretty sure that is what they were doing.
Perhaps "frontrunning"? There's serious money to be made in speed, in being a few milliseconds faster than the next guy.
Michael Lewis wrote a book, Flash Boys, that talks about it a lot:
https://en.wikipedia.org/wiki/Flash_Boys - as it was written in 2014, it would be directly relevant to the conversations you were having with them.
Is there an argument to be made for the HFT adding real value to the system?
Sure. The HFT traders go on about liquidity and market making and a lot of other stuff they claim is essential to a modern financial system.
Meanwhile, the rest of the world thinks it's just a tax on transactions enabled by their paying obscene amount of money for speed, which I think is a good description of it. I'd be all for a "minimum time to hold" requirement on stocks (though there are ways around that), or a small per-transaction fee that made HFT infeasible.
But I don't have the kind of money that the HFT sorts do to throw at politicians to make sure the gravy train continues. And the rest of us pay for it, fractions of a penny at a time.