Feature selection methods not so useful for graphical model structure learning

As discussed in one of my previous posts (here), feature selection and graphical model structure learning are highly related. On one hand, variables in the Markov blanket of a target variable can be used as a compact and effective feature set for predicting the value of the target variable; on the other hand, traditional feature selection methods can used to shed light on the local structures around a target variable (see another post of mine). However, the paper "Local Causal and Markov Blanket Induction for Causal Discovery and Feature Selection for Classification" (Part I, Part II) provides extensive experimental results that support the first practice but question the second practice. The authors found that traditional feature selection methods tend to return variables that are highly predictive but are often not in the Markov blanket of the target variable and therefore not useful in structure learning.