it must be said that what impedes access to sacramental Reconciliation and the Eucharist is not a single sin, which can always be forgiven when the person repents and asks God for pardon. [Not the priest in Confession?] What makes access to these sacraments impossible is, rather, the state (condition of life) in which those who have established a new bond find themselves: a state which in itself contradicts what is signified by the bond between the Eucharist and marriage.
Scola, Marriage and the Family (Emphasis and comments mine).
Although both cardinals defend traditional Catholic doctrine on the subject by arriving at the correct conclusion (i.e., divorced and civilly remarried Catholics are barred from Holy Communion), their rationale strikes me as ambiguous at best and heretical at worst.
The true reason is as pure and simple as the words spoken by our Blessed Lord, who identified such unions as adultery, a mortal sin. Consequently, anyone in a state of mortal sin cannot receive Communion.
I remember reading a Protestant study bible years ago in which the comments made the exact claim that these cardinals are making: that is, that the second union, though sinful at the outset, should not be considered a perpetual state of adultery, which is plainly false. This, to me, is the primary reason for denying reception of the Sacrament.
Only after this primary reason is acknowledged can one proceed to the second reason concerning a person’s “state” in life that is objectively contrary, etc., even assuming that two Catholics cohabiting in such a state are living “as brother and sister.”