The only reason I could personally come up with was that Pink Noise incorporates not only how the driver will perform against the given frequency itself (the one being measured through the sine wave counterpart), but also every other frequency that is produced. Does a driver change how it sounds when other frequencies are present? We really don't know how it'll react in this way. I did do a bit of digging and found this. It's for measuring loudspeakers, but does clearly outline the advantages of using pink noise over a sine sweep
Also, if they were using an RTA program to measure, it's standard, if I'm not mistaken, is actually to use pink noise. An FFT's standard is for a sine sweep. I could be mistaken though.
In-room, pink noise gives a much better impression of how the speaker will sound than a test signal. The pink noise frequency response curve 'sweeps up' all energy radiated by the speaker, on and off axis inclusding the effect of reflections from the floor, wall etc.. Pink noise is not a windowed response, so it can, under optimum conditions, gives a holistic impression of how the speaker performs. An anechoic response that shows a level change across a frequency band may show a flat response when tested in-room with pink noise. Which is correct? Both, yet neither. It may be necessary to back away from a ruler flat anechoic response if listening and in-room pink noise testing show (as they often do) that a ruler flat anechoic response under-reads the total amount of energy sprayed into the listening room.
That's called intermodulation distortion and can be measured separately. It's not an excuse for futzing up the FR measurement.
As for your quoted article that claims that sine sweeps cannot be used for room measurements, just because he doesn't know how to do it doesn't mean it can't be done easily. Maybe he should take some notes from Room EQ Wizard. Never mind that we are talking about headphone measurements not loudspeaker measurements.