I work in a newborn nursery with a level II NICU, and we have secretaries (we call them techretaries--LOL). They have to be CNAs, but their major responsibility is to work the desk--enter orders, make charts, stock the unit, answer the door and phone, etc.
They do some vitals, feed and change babies, take babies out to mother or bring them back to nursery. Some will do blood sugar checks. Some will do the first bath.
They do NO patient care with our NICU babies at all.
I am sure that is why she was saying secretary. If you are familiar with your hospital's order entry system, and don't mind learning how to enter new orders or learning the handwriting of new doctors, or some of the lingo associated with neonatal care, then I don't see why you couldn't do it. Just keep in mind that you won't get to do all the neat sterile procedures, assist with line insertions, dressing changes, drawing blood, etc that you will get to do in adult care.