My wife and I went through 6 years of fertility issues before having our boy/girl twins (now 21 years old) so I know a little about this. We were about to consider adoption.
The grandparents never said anything about wanting to be grandparents, probably because they already WERE grandparents. But I bet that Bill and Hillary, while welcoming an adopted grandchild, would not totally equate an adopted grandchild with one made “the old fashioned way.” I hope that I am wrong, but I know that when my wife and began to discuss adoption, that we’d love our child, but it would be different than “having our own.”
A friend of mine and her husband adopted two children and not long after, her husband decided he liked another woman better than her and the kids so he left.
Subsequently, his parents (the children’s grandparents) do NOT consider the children to be any relation to them and ignore them completely.