The institution can choose grant this account, but doing so does increases the liability risks in the event the member ceases to me a member and access to the business account is not terminated. Further, while the member may have signing authority, enabling their ability to comingle personal and business funds puts the bank on notice of a potential breach of fiduciary duty and could put the bank front and center in the middle of a lawsuit from the other members or from the business' creditors if the member is stealing funds from the business.
Can you give the access? Yes.
Should you give the access? Probably a bad idea.