Well, one tester (and Greg's graph was generated to rebut his graph) was converting each output frame to PNG and then feeding them into one of a number of PSNR tools one by one to get a PSNR result. The conversion from YCb'Cr' to RGB is lossy, but apparently this particular author didn't know that.
He was also using multiple PSNR tools because some were mysteriously not working with some video inputs. Given that there's no one standardized way to calculate PSNR, that led to additional data lulz.
And for x264, he apparently didn't generate his own numbers, he just used someone else's published numbers.
Anyhow, He reported that x264 was 30-ishdB (!) better than Theora. Wha? If every Theora frame was black, that still wouldn't account for that much difference. YUV12 is only 40-45dB deep!
In other words, the whole point of the graph was originally to illustrate and rebut these errors, and it turned out to be a nice regression test too.
Also, for the record, the x264 curve is not perfectly smooth, but that it's as smooth as it is attests to the fact that it's a nicely tuned codec. That Theora is lumpier is one indication it still has more tuning to be done.
Also, Greg's response below is way more levelheaded than mine. He actually collected the data himself (so has more detailed, accurate and first-hand knowledge) and he also probably hasn't been drinking whiskey all night.