[Edi]

I put that part in the FAQ on the word of someone else when it came up in the FAQ Discussion thread. I don't remember who said it, but there was a distinct claim that item-caused afflictions don't heal. It is possible that afflictions caused by hearts can be healed, but that person was very adamant about eye afflictions not healing.

I did not test those assumptions, but editing a commander with recuperation into a map file and assigning one of the heart items and an Eye of Aiming, then hosting for e.g. 30 turns should give some results.