OP, serious question: what are you envisioning your nanny will be doing with your child during the day? What aspects of pedagogy in early childhood education are you expecting her to employ in caring for your baby.
It is FAR more important to find a nanny with great communication skills, who clicks with your family, and has a similar approach and philosophy to childrearing to you. Even these PPs who say they love their college educated nannies? They are all saying these are older nannies who have retired from teaching or similar. The reason they love them is that these are people who have worked with young children for decades. It is their experience that matters, not their degrees.
For infant care, experience and instinct are all that matter. As your child gets older, some experience in ECE is really useful. But it need not be a degree -- great nannies often get this experience in daycare centers, Montessori schools, homeschooling their own children, etc.
You are focusing on the wrong thing. It's the least important credential. You should be grateful your service is being honest with you about this.