fwiw, this uses software [1] that has dozens of dials to adjust yet not giving access to those dials. That's probably why. One of the key challenges (i've tried to write chord detectors personally) is that different instruments sounds have different harmonic falloff rates (in different frequency ranges no less).
I think you nailed it. Yes, the algorithms can't figure out all the proper tuning yet.
For instance, the lowest frequency (among the strongest amplitude candidates) is often the bass line, & thus the chord. However, those type of general rules are common, yet often broken to make the music more interesting in the first place. Esp. when notes are "left out" to open things up & let you mind fill it in.
[1] http://isophonics.net/nnls-chroma