You are entitled to any document that you sign. Furthermore in the footer of the DA FORM 4856 at the bottom it states: Note: Both the counselor and the individual counseled should (key word being should) retain a record of the counseling. It seems very strange that your unit will not allow you to have a copy.
Items to Consider
You might consider asking to see your 1SG/CDR on open door policy to request the copy of the counseling statements. If they refuse to do so consider asking to see the BN CSM/CDR on open door policy. You can also request assistance from your local IG/JAG office