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In the above mentioned note (published May, 2017, this journal), the first and fourth authors proved a local controllability result around the straight configuration for a class of magneto-elastic microswimmers. That result is weaker than the usual small-time local controllability (STLC), and the authors left the STLC question open. The present addendum closes it by showing that these systems cannot be STLC except under a restrictive equality constraint.