Answer: A quick review of my references does not mention iodine in connections with growing radishes. (I did find a reference to supplementing livestock feed with iodine when brassicas are the predominant ingredient, however.)
Perhaps your friend was thinking of boron -- this is sometimes applied as an extremely dilute spray when radishes are grown commerically in high pH, sandy soils. At home it would not be recommended because excess boron is potentially toxic to plants and some plants are extremely sensitive to it.
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