Recent high-precision mass measurements of Li-9 and Be-9, performed with the TITAN Penning trap at the TRIUMF ISAC facility, are analyzed in light of state-of-the-art shell model calculations. We find an explanation for the anomalous isobaric mass multiplet equation behavior for the two A = 9 quartets. The presence of a cubic d = 6.3(17) keV term for the J(pi) = 3/2(-) quartet and the vanishing cubic term for the excited J(pi) = 1/2(-) multiplet depend upon the presence of a nearby T = 1/2 state in B-9 and Be-9 that induces isospin mixing. This is contrary to previous hypotheses involving purely Coulomb and charge-dependent effects. T = 1/2 states have been observed near the calculated energy, above the T = 3/2 state. However, an experimental confirmation of their J(pi) is needed.