Yes livebearer means that they give birth to live young.
I find it very unlikely that your platy had a miraculous conception, she was probably pregnent when you bought her.
I have found when my Cherry Barbs bred that suddenly 'new' babies have arrived, (impossible because there were no fish in the tank to give birth) the most likely circumstance is that these babies are late developers, runts of the litter if you will. They are just much smaller than the rest because the are not dominent, thus not getting more food, also is it possible that you missed all the fry when putting them in the breeding net?
I am not an expert but hope this has helped you.
It is great when these little suprises happen isnt it!