If a character is lying about themselves and has no reason to trust you, then it's good use of the game mechanics to use dice rolls. And that's SH. She can't trust you so to get through to her or get a straight answer you're going to need sense motives and persuasion checks to get through it. If you're going to have a character who just complies to the player because they're the player, then it would be frustrating if they were written as deceptive and untrusting. Her gameplay is good as it's shaped to her characterisation.
This is assuming the approval rating effects the DC of the roll, if not then that would be the solution. As SH is entirely written as a character who kepts things from friends, and there really isn't enough time in the EA so far so even count as that.
Minthara is the best character and she NEEDS to be recruitable if you side with the grove! Also- I support the important thread in the suggestions: Let everyone in the Party Speak