Is returning cholesterol to the liver really performed by HDL?
According to Reverse Cholesterol Transport: Molecular Mechanisms and the Non-medical Approach to Enhance HDL Cholesterol (Frontiers in Physiology, 2018), both HDL and LDL are involved in reverse cholesterol transport. 



In short: HDL takes cholesterol from the blood (from lipid-laden macrophages) and delivers it to the liver 1) via scavenger receptors (SR-B1) or 2) via LDL and LDL receptors (LDL-R). (For a detailed explanation of the diagram, see the Figure 1. in the linked article. There's a similar diagram (Fig.1) in Journal of Cardiology.)

Petter Atti says in his blog (emphasis mine):


  Historically this process of returning cholesterol to the liver was
  thought to be performed only by HDL’s and has been termed reverse
  cholesterol transport, or RCT [...]
  
  This RCT concept is outdated as we now know LDL’s actually perform
  the majority of RCT. While the HDL particle is a crucial part of
  the immensely complex RCT pathway, a not-so-well-known fact is that
  apoB lipoproteins (i.e., LDL’s and their brethren) carry most of the
  cholesterol back to the liver. In other words, the “bad” lipoprotein,
  LDL, does more of the cleaning up (i.e., taking cholesterol back to
  the liver) than the “good” lipoprotein, HDL!


He says that LDL does "more of the cleaning" than HDL, which may be technically correct in the sense that more LDL than HDL particles may be involved, but this alone does not change the concept of good or bad cholesterol. In the image, you can see that the initial cleaning (step 2 and 3) is done only by HDL, so without HDL no cleaning might occur at all.

Low HDL and high LDL levels in the blood are known risk factors for atherosclerosis (NCBI Books, 2019). Not all LDL particles are bad, though, the most harmful are oxidized small dense LDL particles (Hindawi, 2017).