I'm another who was given the injection, retained the placenta and, having delivered naturally and vaginally, found myself being given a complete spinal block and wheeled into theatre to have it removed surgically.
I think retained placentas are a pretty common side effect of the injection. I also think, because I'm a cynical old cow, that the injection is given as standard hospital procedure because placenta-usually-pulled-out-in-20-minutes-and-then-woman-out-of-delivery-suite is a better outcome for the hospital clock watchers than wait-up-to-2-hours-for-nature-to-take-its-course. But like I say, I'm a cynical old cow.
The experience of the injection and its aftermath is a major factor in me planning for a homebirth with independent midwives this time around...
If you do decide to have a physiological third stage, I would strongly advise you to have your birth companions absolutely on the message with it. As you go into transition, your birth partner says to the midwife: physiological third stage! As you start pushing, birth partner says to the midwife: remember! physiological third stage! As the baby crowns, birth partner says to the midwife: remember! physiological third stage! As she approaches with the scissors, your birth partner says "stop! we're waiting for the placenta to deilver before cutting the cord!"
Noone will read your birth plan if you are hospital, and even if they do, chances are that the midwife who talked through it with you will have gone off shift by the time you deliver - you really need to have an advocate there whose job it is to make sure that everything goes according to your plan not their procedure - maybe even worth hiring a doula for peace of mind.
And my IMs this time are indeed suggesting that we go for the phsyiological third stage. If after an hour the placenta hasn't delivered, they have to suggest the injection. They say that I should be able to keep discussing it with them for a good half an hour or an hour, by which time chances are it will have delivered naturally If it doesn't come out, then go for the injection. And if the mother starts bleeding majorly, then they can stop it in minutes with the injection. Seems to me that a physiological third stage with the injection in a box waiting to be used is the best of all worlds.