Why would FFT interpolation using zero-padding undershoot the true frequency of a single tone sinusoid?
The FFT of a strictly real input results in a conjugate mirrored result. For a sinewave, both a positive and a negative frequency peak will appear.  If the input is not integer periodic over the full aperture or is zero-padded, the two response peaks will be Sinc shaped, with lots of extended ripples in the frequency domain.  The positive and negative frequency Sinc images overlap and thus can constructively or destructively interfere, depending on the phase of the input sinewave and/or the window.  For the lowest few FFT bins (and those very near N/2), this overlap can be quite substantial, and thus so is the potential peak shift of the summation.