Recent high-precision mass measurements of 9Li and 9Be, 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(π)=3/2(-) quartet and the vanishing cubic term for the excited J(π)=1/2(-) multiplet depend upon the presence of a nearby T=1/2 state in 9B and 9Be 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(π) is needed.