I think I said "not exactly" in response to "without really working the anti-oxy's". My diet (what there is of any) consist largely of anti-oxidants, unintentionally. Have supplemented ample A, C, E...many others but never noticed any issues if I did not sup on any given occasion while Lugoling. I've amped up the A, C, and E recently (Carlson makes a great mega combo softgel) to see if it helps my resp. probs and the sudden onset of pseudo allergies.
I have my own theory on the reports of undesirable experiences from the use of Lugols, or any of them (dines/dides). It involves the whole "forcing" notion. I believe one must be led by instinct, intuition, and urge - not strict adherence to any specific or demanding protocol.