However, openly encouraging people who are in the state of mortal sin to receive communion is not a good idea. It only makes their situation worse (1 Corinthians 11:27). The Synod is treading on some awfully thin ice.
It's quite true that the priest or other distributor of communion has no idea of the state of the soul of someone who presents himself in the communion line. Unless it's a (very rare) case of a notorious public sinner (and even they may have gone to confession recently), the distributor has to assume that the person presenting himself is in the state of grace.
As far as I can recall from recent or semi-recent events, i.e. the lesbian Buddhist incident comes to mind, priests are basically not to refuse communion regardless of what they know or how public the sin is. From what I have read priests are expected to give communion to any who come up to receive, and that makes these arguments a bit semantic, at best. I mean, the Church officially "admits" all to communion, and so how can that concept be raised now in terms of divorced people. Encourage, as you say, maybe, but that is really not much of a theological concept.