Yes.
> HFTs by themselves can provide liquidity (like any other investor)
Exactly: like any other investor. Meaning, the "high frequency" part of HFT is not what provides the liquidity. (I admit that I should have made that clearer in my previous post.)
Suppose an HFT enters a limit order that is more competitive than the current limit. Either some other investor would have been willing to trade at the same price (as the HFT's limit order), or not. If not, then it doesn't matter how fast the HFT places the limit order; it's going to increase liquidity in any case. So the "high frequency" part is not necessary; the key is that the HFT is an investor willing to trade at a certain price.
But if some other investor would have been willing to trade at the same price, then the only difference the HFT makes is speed: the liquidity gets added sooner than it otherwise would have. So the "high frequency" part doesn't change anything except who the profits from the trade go to.