I don't know the history of their battery division, but Samsung have their fingers in a very large number of pies, from semiconductors to shipbuilding, home entertainment, agricultural machinery, textiles and food processing. Sometimes one division (e.g. electronics, who are the phone makers) use components from others, sometimes they do not.
But one does wonder, given the unusually early Note release and all of the stories that it was pushed forward to get it out before the iPhone, whether some of the testing was cut short in order to meet the deadline. But we can only speculate, and even if that were true it's unlikely that they would ever admit it.
Ironically it also seems likely that this was a year when there was no need to rush to beat the iPhone release. After a long-established cycle of a new design one year, minor refinement the next, it seems like Apple have stuck with pretty much the same design for a third year, just moving the antenna strips a little and removing the headphone jack. I'm looking forward to watching them try to claim that last as a reason to buy the phone, though I'm sure they will try (a lot of guff about how good headphones designed for the lightning connector are, no mention at all of the fact that anyone who wants to make a headphone that works with that connector will have to pay a fee to Apple, and a quick glossing over the crappy little adapter if you want to use your existing headphones with it).