V.W.
There is no "closure for the little one's sake". She is without a father, and yes she will be asking more and more questions... and like any child, will wonder what SHE did to cause him not to love her. There is nothing that will stop those thoughts from turning in her head. It doesn't matter to her whether or not she has a piece of paper saying that he's her dad or not. If there is NO ONE ELSE that it could POSSIBLY be.. then what does the piece of paper matter to your friend? She doesn't want to admit to her daughter that she doesn't know who her father is?
IF your friend wants to retain any kind of legal rights for her daughter (say your friend suddenly loses her income and needs help supporting her daughter, or she becomes ill and insurance and medical expenses become an issue) then the answer is simple. She retains an attorney (or uses state services at reduced cost to her) to file a paternity suit. The court will require him to participate in a paternity test. Some states may of their own volition require him to pay child support... as the support (from both parents) is the right of the child, not the custodian of the child, but she can find out from the attorney whether that applies in her state or if she can sign an agreement with the father waiving it for the time being. He can also be required to provide medical insurance coverage for her.
I do not believe that, once the child becomes an adult, in your "one day when she wants to track him down" scenario, that the child will have any standing to force him to submit to a paternity test. If your friend wants it legal... then she needs to pursue it through legal means. Now. Some states allow paternity testing using Buccal swabs (swab the saliva inside the cheek) for testing, not blood draws.
And frankly, of COURSE he is concerned that she is after more than just the "closure". This is a HUGE financial obligation that will be thrust upon him and moral obligation if he has any (not saying it shouldn't by any means). She may claim to be, actually be, and want to be financially independent of the father of her child forever... but circumstances can change unexpectedly.
The questions her daughter has will not be ANY easier for "knowing" that a test says that man fathered her. But if she opts NOT to pursue confirmation thru legal means... she had better be absolutely certain there is NO CHANCE that it is someone else instead.
As a side note: my gut says that your friend is more interested in not having to "share" her daughter with "Adam" than in being "independent". And that may (or may not) be the best choice for her daughter in the long run. It CAN be amazing (in Some cases) how men can change and "step up" when they find out and are faced with YES, THAT IS MY CHILD. Perhaps your friend doesn't want the potential issues stemming from him deciding to build a relationship and fighting for visitation, etc and is avoiding legal avenues for those reasons. If so, I say shame on her. It is her daughter's right to have 2 parents. Her daughter didn't choose to have only one parent. And I know I will catch a LOT of flack for saying so... but that's just the way I feel about it, in general. Please forgive me if it offends anyone. I don't see a need to sugarcoat the plain facts.
Basically, you are right. There is no "positive all around" outcome.. if your friend doesn't want "Daddy" to be part of her daughter's life. And even if she does, there are no guarantees there, either.
Good luck to your friend.. and best wishes for her daughter.