I can check them out, but you can probably use both - meaning one can be used as a diversity statement(unique situation/experience) Won't be able to know for sure though until it's been read obviously :)
... everyone's throat any possible diversity I might have"- probably means ... immigrant parents. In some ways diversity has become a cliche (understand ... meaningful. That can be a diversity related topic for sure!! But ...
When you say you have lived and studied "here" your whole life, is that referring to UK or US? If you've lived your whole life in UK, then I think you can absolutely make a diversity statement out of that.
@DEC_LSAT If I had thousands of applications to read, I'd be irritated (1) by someone overselling her "diversity", and (2) by someone who made me read an essay that didn't tell me anything relevant or interesting.