If a woman I was interested in suggested that I come to meet her counselor/therapist, I would be pleased to do so, for more than one reason.
First, the purpose of going to a therapist is (hopefully) to get help and insight. A good therapist does not (in fact can not) make decisions for his patients, but rather tries to help them see things they have trouble seeing themselves and to teach them tools for dealing with certain types of problems. (Often there is a support component as well, of course - or occasionally the two-by-four upside the head when called for.)
One of the difficulties a therapist has is that virtually the only source of information available for achieving understanding of a patient's situation is what the patient him- or herself reveals - and this is often both incomplete and distorted. A romantic relationship tends to have a significant impact on a patient's life, but what the patient reveals about it is often rather misleading. Meeting the person in question can potentially provide the therapist with a very useful new point of reference.
Beyond that, though, I value the insights and advice of my friends, my family, and yes, my therapist/counselors. Why would I want to deprive myself of those benefits when it comes to something so important as a prospective partner? And why would I want to deprive my prospective partner of those same benefits? Yes, the decisions we make must be our own, and are not conditioned upon the approval or support of others. But if you can't trust a friend to give you good advice, then why do you have that person as a friend anyway?
Furthermore, I cannot understand the idea that it is a good thing not to be asked to meet a prospective partner's friends. If I'm interested in a woman, I'm interested in sharing her life, and that means I don't want to be kept in some separate compartnent. If I can't get along with her friends, then something's wrong - and it's better to make that discovery sooner rather than later. In fact, if she doesn't want me to meet her friends, I have to wonder whether she's ashamed of me - or ashamed of her friends. Either way, something's wrong.
If I'm interested in a woman, I want her to meet my friends. Heck, I want her to meet my parents!. Not because I don't trust my own judgement, but because I do trust both my judgement and theirs. I expect them to approve, both because I know that they have confidence in my judgement and because I expect them to see at least some of what I see.