I would say that most scientists, at the top of their game, who have years of trusted publications behind them, should be given some latitude to publish discovery science without the requirement of reproducibility, so long as they share their results in detail, and accept postdocs who then take the resulting research materials to their new labs.
I didn't always believe this, but after spending a bunch of time reading about the numerous times in history when one scientist discovered something, published the results, and were told they were wrong because other people couldn't reproduce their results, only to be shown correct when everybody else improved their methodology (McClintock, Cech, Boyle, Bissell etc).
This ultimately came to a head when some folks critized the lack of repeatability of Mina Bissel's experiments (for those who don't know, she almost singlehandledly created the modern understanding of the extracellular matrix's role in cancer).
She wrote this response, which I originally threw on the floor. http://www.nature.com/news/reproducibility-the-risks-of-the-... After rereading it a few times, and thinking back on my experience, I changed my mind. In fact, Dr Bissel's opinion is shared by nearly every top scientist I worked with at UCSC, UCSF, and UC Berkeley. The reason her opinion has value is that she's proved time again that she can run an experiment in her lab that nobody else in the world is capable of doing, and she takes external postdocs, teaches them how to replicate, and sends them off to the world. In other cases, she debugged other lab's problems for them (a time consuming effort) until they could properly reproduce.
I believe reproducibility is an aspirational goal, but not really a requirement, for really good scientists, in fields where reproduction is extremely hard.