Can a strong electrolyte be sparingly soluble? A strong electrolyte is an electrolyte that completely, or almost completely, ionizes or dissociates in a solution. 
My book has a question:


  In a saturated solution of sparingly soluble strong electrolyte $\ce{AgIO3}$ the equilibrium with sets in is $\ce{AgIO3→Ag+ + IO3-}$


Is the above statement wrong or is there anything as sparingly soluble strong electrolyte?
It means that by just adding it to water wont make it dissociate into ions(sparingly soluble) but if current is passed through its solution, it will easily dissociate and give ions. These cases look rare.   

But Curt.F's reasoning looks better :  


  In the low concentration regime where the salt is "soluble", it completely dissociates, but that the solubility limit is just low.