However, isn't it about Building Relationships of Trust? Missionaries are taught, in the MTC, to look for common themes and finding way to build trust with their investigators.

Shouldn't a missionary also implement this same technique with members of the ward he is called to serve? If I personally was not able to have some level of trust with a missionary, would I entrust him to share the gospel with non-member friends or family?

I agree that the gospel is still true, whether or not, a missionary likes BYU or not. Would I still send referrals to the missionaries? Yes, of course I would. I am simply saying that this missionary did not help his cause in building relationships of trust with members (even if it may have been just one member) of his ward. I'm just saying that it was an NOT the right forum for him to express his feelings regarding his dislike for BYU.