From the referenced study: "The measurements were conducted in a diffuse sound field at a reverberant noise chamber at the NIOSH acoustic testing laboratory. The diffuse sound field ensured that the location and size of the smartphones did not influence the results of the study. "
Having done sound testing extensively, you can be sure in an airplane positioning and sound source and sound type can drastically impact your measurements. Multiple reflections can re-enforce, or reduce the measured level. The type of sound measured is very important as well.
He's not measuring pink noise on the airplane, what the measured level of a particular sound is, needs to be normalized to really understand what effects it will have on you.
I'm sure in a good test setup the smartphone can get you pretty darned close. I'm more concerned with this guy's test setup than the equipment used.
Actually, if you pick the correct app they are surprisingly accurate: http://scitation.aip.org/content/asa/journal/jasa/135/4/10.1...