> Now in the particular problem I am working at, we have a couple of fits like [5] and some of them have a slightly worse reduced chi square of say about 1.4 or 0.7. At this point the two methods start to deviate and I am wondering which would be the correct way of quoting the errors estimated from the fit. Even a basic reference to some text book that explains the method used in scipy would be very helpful.
I didn't look at your data, but I guess that these values of the reduced chi square are still in range such that they are not a significant deviation from the expected value of one. The chi-squared distribution is rather broad. So I would omit steps 2 and 3. Only if you have good reasons not to trust your assumptions about the errors of the data, then apply steps 2 and 3.
We looked at which part of the CDF these values are and they are still ok. And our errors are all inferred from measurements, so we trust them quite a bit. We use the fitting described to obtain a particular property of an ion via spectroscopy... that's also why we want to get our errors on that property correct :)