I don't think it sounds unreasonable at all and many poly couples have similar boundaries. If meeting her potentials before she is to venture past a certain point is a boundary for you, and she needs to respect that in order for you to feel comfortable with her having outside relationships. If that is a hard boundary for her and she would rather not date at all, then to stay in a relationship where you feel comfortable, I guess it is more important to her not to have you meet guys than it is to date them.
She may have a point about believing you have a hidden intention to get into a penis measuring contest, but it is my opinion that she should at least give you the benefit of the doubt once or twice before just assuming. It isn't fair not giving you a chance to prove you can do this maturely and that you have no hidden intentions. I don't know you well enough to know if this is the type of thing you would do or not. If you convince her to let you meet her potentials, then it will be up to you to make sure to treat them with respect and put her fears to rest.