If the cost really is only $20k, I find it hard to believe that RG finds this small price to be unreasonable...
If you accept that this use does not qualify as fair use then in good conscience you can only display the lyrics for which you have purchased a license. That cripples the coverage you can provide by making it too resource-intensive to seek out a licensing agreement for the lyrics of more obscure songs.
The question is this: Do the founders wish to be provocative and make a point about the music industry, or do they want to avoid friction? After watching a few interviews with the founding team, I wouldn't be surprised if it was the former.