I don't know what the official policy is, but the human in me thinks that if the lady is uncomfortable breastfeeding that is her issue and she should take measures to accomodate her "nervousness". Inconveniencing other people is selfish and inconsiderate.

I probably would not have moved. Not sure what I would have done if the FA insisted, but given the fact that you specifically purchased that seat, I would have stood my ground - and been fairly upset about it.

The FA later telling you you didn't have to move sounds like an apologist. Kind of like when one person backs out of an event cause there aren't enough tickets, and only afterwards do people say "oh you didn't have to do that..." just to sound gracious.