They also regularly reiterate that the index is meant partially in jest, and that you shouldn't expect it to generalize in any kind of highly accurate way. Also, the leap from forex to inflation is a big one; AFAIK they haven't argued the data is valid to use as you are here, which is different from judging exchange rates (it must surely be normal for various kinds of goods and services to inflate differently, right?). They simply point out that it works surprisingly well for something so simple.

Even assuming the 2% numbers are more representative of the average household, the 4% big mac number sounds entirely consistent with that.

TL;DR: this is interesting, but I don't see how this data clarifies anything.