We have two joint applicants. Co-borrowers credit stinks. We offer to do the loan in primary's name only. Loan is done in primary's name. This is similar to a counteroffer except even though the primary applicant excepted our counteroffer wouldn't we still need to send a denial to the co-borrower???

I would say yes, you would.

Absolutely. You are denying the co-applicant so s/he deserves an AAN.