What isn't pointed out in the BBC article is that having an epidural raises the risk of needing forceps or having a slower labour - the 2 biggest risk factors associated with muscle damage.
Yes, this study showed that women with epidurals did better overall, but I would wonder how the women were chosen for the study. 33% CS rate is enormously high, so possibly these were higher risk women or women at a hospital which pushed interventions. And when you take out the CS women, it's not that big a study to be comparing outcomes.
The study author mentions that pushing too much, too soon without an epidural could be a reason for damage. Well, with a well monitored MW attended birth, with a women who has done antenatal classes (where they talk about not pushing too soon and how to help control this) you should reduce the risk of this happening anyway. Active and water births could also reduce the risks associated with a long second stage by helping you and the baby to get into optimal positions for pushing.
It's interesting, but it certainly isn't sufficient evidence to have an epidural purely on the basis of not wanting to risk your pelvic floor muscles, particularly as it's known that having an epidural means you're at higher risk of needing interventions and having a longer labour.
It does make an argument for doing more pelvic floor strengthening work before and after birth and attending good antenatal classes to learn about how and when to push. Also having a good birth attendant so that you can get guidance on when to push if you need it.