I don't know anything about the "Your baby can read", but I sang fun and learning songs and read books to my all of my six children. From the beginning. I sang the abc's and 123's at home. Later we graduated to books and paper when they showed an inclination to pick these up and use them. When my children started school, they already knew a lot of the material and I believe this helped them to feel more confident when they began school.
But you have to take each child as they are. Our second son had ADHD and learning through visuals in educational movies and educational toys was the only way for him. He could not sit through a book and he could not take verbal instructions well. However, he would sit down with any computer toys and learn from them.
I believe if you make learning fun for your child from the start, with songs and reading for pleasure, they will gain a love of learning from you. But you can take a good thing too far, I would not shove learning down their throats by doing lessons to excess. This might sour them on learning. Keep it light, fun and geared towards the childs basic needs and all will be well. Good luck! : D
Babies arent supposed to read. Let kids be kids, let them be thier age without all the crazy pressure to be more and more and more. You should only worry if they arent hitting normal milestones within the right time range.