I suspect that a good number of such nuns and priests had not devised these ideas themselves but had gotten these ideas from moral theologians. (I am not claiming that any particular idea is authoritative or binding enough to count as a “rule,” now or in the past.)
I don’t have specific theologians or sources in mind, but here are a few online mentions and a few different views:
Communion for Late Arrivals at Mass? (Fr. Edward McNamara)
It is true that before the Second Vatican Council some moral theology manuals placed arrival before the offertory as the dividing line in deciding whether one fulfilled the Sunday obligation of assistance at Mass. But after the liturgical reform, with its emphasis on the overall unity of the Mass, modern theologians shy away from such exactitude.
There were different views about limits on lateness, or presence at Mass. In one view, moral theologians thought that you had to be there at least for the reading of the Gospel onward. A good view. The Gospel is important. In another view, you had to be there from offertory onward at least under the purification of the chalice after Communion.
Others will say that you have to be there from the first words of Mass to the very end. A laudable approach, though a little inflexible.
(Fr. Z prefers “the old chalice veil to chalice veil idea” and gives reasons, but he is also “not comfortable with the minimalist approach” in terms of “our involvement.”)