Hello Jean.
I find your statements very confusing.
I would want to know who the holders of the papers she was granted some access to were / are. State, Charitable institution, Christian Social Services, Private etc.
Then seek advice re the governing legislation of the period of adoption, and subsequent legislation covering the held material. Much has changed over the years, re the holding of such material, and who may gain access, and under what conditions. Including the ability to have a support person when accessing the material.
My interpretation is that your cousin has found some papers re her adoption, which she has been granted a "limited" viewing of. Not “granted her papers”.
For a number of years, I was involved in an adoption support group, and worked through the system, of that time, re adoptions. Plus experienced changes re the introduction of the Family Court etc which encouraged more "open adoptions".
Adoption files can contain more than just the basic formal questions placed upon the parties involved. Those questions can include a personal preference sheet, nominating a faith based upbringing, rural based upbringing, music background, sport, academic etc. These can hint at the aspirations of the birth mother.
They can also contain personal correspondence sent to the agency involved, for handing over, for the benefit of the other party. Photos, gifts, etc. Such material may have contained a request that the material be made available at a milestone etc. Christening, 1st, 5th [going to school] birthday etc.
Some adopting families were receptive to receiving such material, others were not. Hence it still being held on file.
Alan.