Why does a brown paper bag speed ripening

Yeah, I would agree with the people in the comments, and make the assumption that it had to do with concentrating the ethylene gas from the bananas.

After a bit of googling, it looks like the rice bag trick might be popular because it apparently results in a nearly ideal, stable environment for ripening.

I imagine that the rice would keep the moisture level at a lower point, the bag would contain the gas, and the mass of the rice would decrease the temperature variants (assuming that is conducive to ripening)

I found an informative article which mentioned rice bags here: http://monsterguide.net/how-to-ripen-bananas-quickly

For Apples, see:

• The Role of Ethylene in Determining Apple Harvest and Storage Life, in the May 1986 Post Harvest Pomology Newsletter, Vol. 4(1)

There are also various websites that give instructions if you'd like to do experiments yourself (generally geared towards classroom instruction):

• http://chemistry.about.com/od/chemistryexperiments/ss/ethyleneexp.htm
• http://botany.org/bsa/misc/mcintosh/badapple.html

... but for a more complete list, go to Google Scholar, and search for 'ethylene' + whatever fruit you're interested in; you'll find stuff going back many, many decades.