"But whichever source you decide to trust, one conclusion is unmistakable."
Uh, not really? Only if you use PPP as a method, if you use nominal GDP or as above-mentioned GNI(the so-called 'Atlas method' that the World Bank provides), the picture changes.
If you use nominal GDP or GNI you should use it with a smoothed exchange rate of 5 years or so to avoid the volatile shifts. But increasing or decreasing your economy by 20 to 48% using PPP isn't a winnable argument for PPP as described above.