A victory for curve fitting

I have previously written many posts (rants?) about the dangers of curve fitting. In particular in one of the first posts The naked truth versus self deception I stated

 I believe that any significant physical effect/discovery should be able to be seen by the naked eye in the experimental (or computational) data and should not require curve fitting.

However, the graphs below represent a significant counter example to my view.

The data is considered to be consistent with the upper solid curve.
This is the data which ultimately led to the 2011 Nobel Prize in Physics.
When I see such graphs I am immediately skeptical. But the authors and the broader community were not and subsequent measurements supported the original claims and parameters deduced from this data. In particular the graph below [taken from a Physics Today article Supernovae, Dark Energy, and the Accelarating Universe by Saul Perlmutter]  shows how several independent methods constrain the parameters.

I am curious to hear what others think.