Access Problem

About the Theory of Mind debate, it is known that both theories (theory theory and simulation theory) share the same assumptions despite their differences. One of them is the "Access Problem", that is, both TT and ST set the central problem as that of gaining access to other minds that are hidden behind the observable behaviors.

How should we deal with the access problem? Shaun Gallagher says:

[T]he basic claim that I will defend is that in most intersubjective situations we have a direct understanding of another person’s intentions because their intentions are explicitly expressed in their embodied actions, and mirrored in our own capabilities for action. For the most part this understanding does not require the postulation of some belief or desire that is hidden away in the other person's mind, since what we might reflectively or abstractly call their belief or desire is expressed directly in their behavior.
[Gallagher, S. (2005). How the Body Shapes the Mind. p.224]

This is true. However, if we stress too much the impact of direct social understanding, we are easily inclined to conclude that it is able to remove the access problem from the research agenda. This cannot be the "solution" to the problem of other minds. The experience of the other person does NOT always provide us with a FULL understanding of that person's mind. A comprehensive account of social cognition, even though it admits the possibility of direct understanding of the others based on the direct social perception, should address to and give an account to the access problem.
[cf., Miyahara, K. (unpublished). Direct social perception and the problem of access to other minds.]

How is it possible? Going back to the experience itself, there are even cases that the deeper experience of the other I have, the more undecipherable she appears...