think your right about it being a problem with the tuner, that its possible aliasing throws the tuner off and that the tuner may be optimized for guitar frequencies. I used it to try and check the pitch of some of the AKWF fm waveforms and it could not even register that a note was playing. If I use the perfect waveforms the note always shows.
being a scientist, i can't resist to bore all of you with some theoretical details regarding this
especially for fm sounds is makes perfect sense for the tuner not to register the basis frequency at all, if you consider how fm spectra differ from those created by a plucked string instrument. for plucked strings, you always get the strong "base frequency" (first mode of oscillation) and only the overtones above that (being integer multiples of the base freq). an example can be seen at the bottom of this page: fixed string vibration
fm spectra look kinda different, as can e.g. be seen here: fm spectra in the second picture. first, the spectrum is always symmetrical to the base frequency, and second, depending on the modulation index, the amplitude of the base frequency might be smaller than that of the sidebands (look at modulation index 2 in that picture, for example). in addition, you might get aliasing effects if the sidebands go above/below the possible range of sampled frequencies.
hence it's not surprising that the tuner which probably just looks for the lowest/maybe strongest frequency component has a hard time recognizing the base note.