i am confused, Alaska customer service is telling me i can't use ONE GGU on a redeye with a connection the following day???? (they want a second for the connection)

She said she confirmed with her supervisor that ALL flights must leave the same calendar day.

She said she would add a note in my reservation that if i change to the earlier non red-eye flight with same day connection if they become available they would "reuse" the original GGU.