Luckily, "Snopes" Editor, made the retraction explanation clear as mud:
(Anybody with half a brain knows the very last line, is the only one ever needed)
Editor's Note: We received a ton of comments in a very short time challenging our assumption that wearing a hard hat "backwards" means wearing it with the brim facing to the rear, and "forwards" means wearing it brim to the front. On the basis of that assumption, we originally rated the claim that Biden was wearing a hard hat backwards as false.
The prevailing counter-argument is that if the suspension of the hat has been purposely configured by its owner such that the bill and tightening knob are worn to the back (as was the case of the hat Biden wore), to wear that hat with the bill facing forward is, practically speaking, to wear it backwards. Therefore, it's argued, it's actually true that, in the photo op discussed below, Biden was wearing it backwards. The strap and tightening knob, which should have been behind Biden's head, were on his forehead.