Is it scientifically verified that bananas will ripen faster when kept in a bowl with other fruit?
I think you've got this mostly backwards. The reason not to store bananas with other fruit is that the ripening bananas emit a lot of ethylene gas and will cause the other fruit to spoil more quickly. You can also use this to your advantage: got a pear that you want to ripen quicker? Put it in a paper bag with ripe bananas overnight. 

Other fruit emits ethylene as well, but generally in large quantities only when they are already quite ripe.

Here is a pretty good reference: http://www.csmonitor.com/2006/0531/p15s01-lifo.html