In general, both of the positions "It's all my fault" and "I had nothing whatsoever to do with this" are, equally, both irrational and cowardly for any of the involved parties.
Even after their children reach adulthood, parents like this may have a very hard time trying to not cater to their adult child's every need - or even his or her every whim. While still complaining about it to everyone else.
A truthful statement would make the parent feel even guiltier for wanting to be free of any family burdens. The parent would probably deny these feelings anyway, because the parent is under the mistaken impression that admitting this would drive their children even further away.