Recent high-precision mass measurements of Li9 and Be9, 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 Jπ=3/2 - quartet and the vanishing cubic term for the excited Jπ=1/2 - multiplet depend upon the presence of a nearby T=1/2 state in B9 and Be9 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 Jπ is needed.