On what basis? You are not their guardian, nor even the parents guardian. Any law purporting to grant you the right would be abusive to common-law, and merely a wrong-headed generation of a law to enforce a generally good idea.
Except in extreme cases (ones which would cause consideration of guardianship), it is the parents full right and responsibility to determine the extent to which you may be involved. They are responsible for that judgement. With all due respect, I think involving the courts in such is, more than anything, being pissy.
I would hope that parents - even those that don't get along with their parents - give the chance for the bonds to grow between grandchildren and grandparents (for a multitude of reasons), but it is certainly not the place for the government to intervene between the parent and their child.
....End of debate!
At the same time, and I think this is more to the book's point, I really have to question the wisdom of parents who Won't Let Their Kids See Their Grandparents. Unless there is some really good reason for going to this extreme (i.e. the grandparent in question is him/herself abusive, etc.), it seems unwise. In the case described in the article it's difficult to think of a good reason from what is told for why the mother should allow no contact with the grandmother whatsoever. I suspect that in many such cases there is an element of "revenge" or "getting even with" a former spouse which drives a divorced parent to cut off grandparents. Seems to me that the lesson to be drawn from a book like this is not that laws are required, but simply that parents really ought to think twice before taking that step.