I don't think any of the narrations are 'mistaken'.
Even the Synthesis transcend mortality itself, may be over a period of 1000s or 10,000s of years.
The idea of 'inevitable' just is that something of that nature is bound to happen at some point. It's just that as Shepard, we can decide whether to aim for it starting now, instead of temper but still pursue it with Control, or sticking to the longer path with Destroy.
Even realistically here, humans as we understand them will not exist forever. We'll either all be killed off, or work to keep ourselves in our current forms, or naturally (as in organically) evolve into what we might consider other species, or incorporate enough tech into ourselves that we may be considered something else (cyborg), or merge ourselves so much with technology that we are one with it, or something else entirely.
Your own opinions on how that might either eliminate or improve 'humanity' and the concept of mortality may vary (is mortality dying of aging? dying ever? no longer having a presence in the universe?).
I believe SynthesisEDI talks of mortality in the broadest terms - that with organics (particularly humanity) and synthetics (particularly the Reapers) working together, they may one day transcend the limitations of the universe and ensure that everyone is able to have a presence in the universe forever, or even beyond it. It's about breaking boundaries and making dreams come true. Or nightmares.
The biggest worry about Synthesis, as it is shown to us and not through more vague hypotheticals or theories, is that advancement of this nature and this fast, isn't what we ought to be going for. That there's nothing wrong with staying mortal (like I was saying, YMMV) and valuing your individualized limited existence and maybe the cooperative existence with others. That is it through temporary life, that we make sure we are people who at least try harder to make correct decisions, not just the most logical or inevitable. Synthesis might one day take that away from us, and we become an utterly alien form of life that does not cherish what we currently consider good and even sacred.
And instead of actually taking lessons from the past and even dwelling on them (which can sometimes be a good thing), we just keep them in our memories and focus entirely on moving more and more forward. This may end up utterly removing the 'humanity' from us, for all we know, and EDI's speech at least gives me a feeling of that. She is alive, we are alive, and we are not alone - but what will we become?