Part of the issue with fact checkers is how charitably they are interpreting the words. For example:
Weather Reporter: The sun will rise at 6 AM Tomorrow
Fact Checker: False. The language talking about sun rise is implying that the sun rotates around the earth, and that has been known to astronomers to be false for centuries.
In her video, Lila Rose is saying that abortion as defined as intentionally killing the fetus is not medically necessary.
From the captions on the video: "Now, you could perhaps do an early delivery if she's experiencing or she has a very severe condition that you need to deliver that baby early, but in that situation you don't go in with a needle or forceps to destroy that baby before birth. You give that baby a fighting chance, and that is not an abortion."
She is saying that the baby may die as a consequence of early delivery, but the goal is early delivery, not the destruction of the baby.
Fact check says "Certain medical conditions such as placenta previa and HELLP syndrome can make abortion a necessary medical procedure in order to prevent
the mother's death."
My guess that Lila's response would be that that it is the early delivery that is saving the mother's life, not the abortion. The mother's life would still be saved if the baby survives through appropriate medical care.
I don't know if Lila is Catholic, but a lot of her reasoning seems to fall under the "Principle of Double Effect."
http://sites.saintmarys.edu/~incandel/doubleeffect.html
"Classical formulations of the principle of double effect require that four conditions be met if the action in question is to be morally permissible: first, that the action contemplated be in itself either morally good or morally indifferent; second, that the bad result not be directly intended; third, that the good result not be a direct causal result of the bad result; and fourth, that the good result be "proportionate to" the bad result. Supporters of the principle argue that, in situations of "double effect" where all these conditions are met, the action under consideration is morally permissible despite the bad result."
The argument is that doing a delivery with intention to save the mother's life is good, even if it has the consequence that the fetus dies, since the death of the fetus was not the intention, and thus would not be called an abortion, since the fetal death was a secondary effect and not the primary intended effect.
The issue with the fact check is that the fact-checkers were so eager to label something they disagreed with as false, that they did not appreciate the nuance.