The main issue is that there are three choices and Puerto Ricans haven't indicated a strong majority for any of the three choices (as often happens in three-way elections). I don't think it's really gotten to the point where Republicans can be accused of having interfered.
I think the US and Puerto Rico should agree to a referendum in say, 2020, which would provide for Puerto Rico either becoming an independent country or joining the union in 2025.
Here's an article on 2012 non-binding referendum.
http://edition.cnn.com/2012/11/07/politics/election-puerto-rico/index.html?iref=allsearch