The problem with using reason is that you need something to reason
from Rationalism works well with formal axiomatic systems where the starting points can be defined to be "true". For dealing with the world we perceive, however, we need to discover the starting points - and that is where empiricism comes in.
Revelation we may also dismiss in that it is clearly unreliable. Someone who believes that they have a personal revelation might consider their revelation to be true but even then they must consider the possibility that others, with conflicting or even false revelations felt the same way.
The point about the scientific method is that it is it takes precautions to guard against error. Repeatability avoids the problems of anecdote and with the selection of data. Alternative health testimonials are anecdote complicated by selectivity - both in the data reported, and sometimes in attribution of the result, too - and the placebo effect as well.
LindaLou's problem was bias, which resulted in her preferring sources which said what she wanted over those that did - ignoring the fact that the sources she rejected were more reliable, by far, than those she accepted.
This is not to say that we cannot use unreliable sources if they are all we have. But we must recognise their unreliability, and use better srouces when they are available.