But on your original point - yes, having entered the Republic of Ireland, anybody can then freely cross the Ireland/Northern Ireland border, since this is open thanks to an entirely separate (ie non-EU) bilateral agreement between the UK and Ireland - the Good Friday Agreement.
However, one of the (many) outstanding questions still to be resolved in implementing Brexit is the nature of the customs (and possibly other) checks between Northern Ireland and the rest of the UK. There will undoubtedly be some, but the detail is still to be negotiated.
But my point is that EU residents only need to show their passport to cross from their mainland into Ireland. Their passports are not stamped, so such travel would not show when they climbed onto a plane to fly from the UK to the US.
That gives them a clear workaround.