Marriage is a public action. If the priest is aware of parishioner who has remarried without a proper annulment then he is duty-bound to not give them communion. If they are married, then we can assume there is sexual relations. If there are sexual relations and a unresolved marital relationship with another person then that is adultery. It is a scandal to do otherwise.
The priests and bishops all should publicly advise in their homilies about the need to receive with a properly cleaned soul. The problem with this latest document is that it muddies the water rather than making things clear. Frankly far too few priests give good homilies. My own experience is week after week of “do what is right, find God’s will for you, blah blah blah” without giving clear, concrete direction on what the Church teaches are right and wrong.
How would this priest KNOW whether or not a “proper annulment” has been granted?