The same brass that shaves lead will result in a bullet that is loose and turns after seating? Or some pieces do one and some do the other? If it's mixed brass, I've noticed there are pretty clear differences in brass thickness. As an example, Remington revolver brass for me seems super thin. It sizes very easily, and has the least neck tension vs the other brass I have.

If the same piece of brass shaves lead and then leaves the bullet loose, perhaps it still has a bit of a crimp in the end and needs the mouth opened up more? I find the "M-style" neck expanders that Lyman, Redding, and I believe RCBS and Hornady use are much better for seating lead than the belling type die Lee uses.