What's intended by "Let the data speak for itself"? In reading the following paper, I came across the following statement:

As mentioned, it is often presented without any reference to probabilistic models, in line with Benzecri [1973]’s idea to “let the data speak for itself."

(citation is from J. P. Benzécri. L’analyse des données. Tome II: L’analyse des correspondances. Dunod, 1973.)
From how I'm reading this paper, it sounds like "let the data speak for itself" means something along the lines of considering various measures across the data without regard to a likelihood function or data generating process. 
While I've heard the quote "let the data speak for itself" before, I haven't given hard thought to what is implied. Is my above interpretation what's canonically implied by this quote? 
 A: Back in around 2005 when "Data Mining" was the latest threat to the statistical profession, I remember seeing a poster with "Data Mining Principles," one of which was "let the data speak" (can't remember if "for itself" was included). If you think about algorithms that might be considered "Data Mining," apriori and recursive partitioning come to mind, two algorithms that can be motivated without statistical assumptions and result in pretty basic summaries of the underlying data set.
@Ben understands more of the history of the phrase then I do, but thinking about the quote as cited in the paper:

MCA can be seen as the counterpart of PCA for categorical data and
  involves reducing data dimensionality to provide a subspace that best
  represents the data in the sense of maximizing the variability of the
  projected points. As mentioned, it is often presented without any
  reference to probabilistic models, in line with Benz´ecri [1973]’s
  idea to “let the data speak for itself.”

it appears to me that the procedure of MCA does resemble apriori or recursive partitioning (or hell, the arithmetic mean for that matter) in that it can be motivated without any modeling at all and is a mechanical operation on a data set that makes sense based on some first principles.
There is a spectrum of letting the data speak. Fully bayesian models with strong priors would be on one end. Frequentist nonparametric models would be closer to the other end.
A: The interpretation depends on context, but there are some common contexts in which this comes up.  The statement is often used in Bayesian analysis to stress the fact that we would ideally like the posterior distribution in the analysis to be robust to prior assumptions, so that the effect of the data "dominates" the posterior.  More generally, the quote usually means that we want our statistical model to conform to the structure of the data, rather than forcing the data into an interpretation that is a non-verifiable structural assumption of the model.
The particular quote you are referring to is supplemented by the additional quotation: "The model must follow the data, not the other way around" (translated from Benzécri J (1973) L’Analyse des Données. Tome II: L’Analyse des Correspondances. Dunod, p. 6).  Benzécri argued that statistical models should extract structure from the data, rather than imposing structure.  He regarded the use of exploratory graphical methods as very important to allow the analyst to "let the data speak".
