As one data point, the headphone jack-having iPhone would drive 26.39 mW into 33 ohms, which means that at max volume you'd be damaging your ears at a volume of around 100dB with the 300ohm impedance and 105dB/mW SPL.
So yes, the previous poster could conceivably be doing the thing that they said they were doing.
Their sensitivity is only 97dB/mW. But I think it's more complicated than that. The amplifier might be able to deliever 26mW into 33 ohms but can it deliver that into 300 ohms? It would have to be able to produce high enough voltages. Also the impedance goes up to almost 600 ohms at the resonant frequency of the headphones, requiring even more voltage [1]. You'd obviously get some sound and it would probably even be loud enough, but there would likely be a significant effect on the frequency response and possibly more distortion that you'd like.
So yes, the previous poster could conceivably be doing the thing that they said they were doing.