Antioxidant supplements provide no benefit, may even be harmful. See 2007 meta-analysis by Goran Bjelakovic, Dimitrinka Nikolova, Lars Gluud, Rosa G. Simonetti, and Christian Gluud, published in JAMA:
“Mortality in Randomized Trials of Antioxidant Supplements for Primary and Secondary Prevention: Systematic Review and Meta-analysis”.
If an actual nutritionist says you can eat it every monkey in a lab coat knows they can sell it as a lotion with substantially less work than testing something else.
Buddy of mine did research in Milan on common sunscreen ingredients. In a lab, those chemicals didn't tend to cross the dermis.
But put that person in the sun and you find detectable quantities of those chemicals in serum within minutes. Turns out the flushing (i.e. rushing of blood to the skin, in particular, to the surface of the dermis) increases permeability. Nobody really tested those chemicals for intravenous use.
So in a very real sense, you ingest in all but digestion the ingredients in your lotions.