In essence, this is a very fortunate and evolutionary development which allows you to get really clear about the actual nature of your relationships. This trust business has given this benefit to thousands of people. Friends and family members whom we thought were really like-minded and trustworthy were not so much; and others whom we doubted were actually more like-minded and more trustworthy than we thought. It reveals who your true friends are.
The best kind of person to fulfill your trustee role is one who is both spiritually harmonious and intellectually comfortable with the role. Gaining a degree of comfort is not necessarily dependent upon having a lot of knowledge about how to be a trustee. It really has more to do with how much that person trusts you, and likewise, how much he or she trusts himself or herself. Hence if you really wanted someone to be trustee but she has doubts and fears about it, it may be that no amount of discussion and reasoning about it would change her mind . . . because perhaps there is something fundamentally lacking in her spiritual harmony with you or her own trust of herself.

Hopefully that perspective about her is incorrect, and it is simply a matter of her not having sufficient information about the role. She really needs to know that there is hardly any work to do, and there is really no liability and no risk to her. But the fact that she is expressing doubts and resistance without even asking more detailed questions about the risk, and the fact that she wasn’t even willing to discuss it, is what indicates that no amount of discussion or favorable information would change her mind.

It also means that even if you were able to persuade her to say “yes”, she might turn out to be not such a good trustee, because she may continue to suffer from unreasonable paranoias, no matter how much you try to show her that they are unreal.
That is where the universe is giving you an evolutionary experience . . . in gently influencing you to reconsider. Perhaps there are other people in your sphere of friends and acquaintances whose virtues and compatibility for the trustee role might be more than you had considered at first.