> It seems off to blame this exclusively for their performance problems

There are definitely ways to improve the performance, but you can't measure them since Heroku gives you no way of determining how much time requests spend in the in-Dyno queue. Tho you can modify your app to get New Relic to display this info: http://rapgenius.com/1506509

> What seems particularly odd is that rap genius appears to be using their Heroku dynos to serve their css, javascript and certain images. So loading the homepage appears to make about 12 requests that hit their dynos, rather than 1.

These assets are Cached in Varnish. We serve them without hitting dynos at all