While technically true, this really doesn't change the question. Life is a complex series of chemical reactions; death is what happens when these reactions stop.
Let's say you die of heart failure. Your heart stops pumping blood. Then the brain stops getting oxygen, due to the lack of blood. Then rigor mortis, and so on. If these aren't all fixed, you would also re-die immediately (actually, without the brain function being fixed, you would never really be alive again).
The premise assumes that all of that has been addressed by them coming back to life. Adding a few external factors doesn't change that. If it did, the simple fact that most people are buried and would suffocate would render the point moot. Same for decomposition.
Although cremation would be awfully hard to tackle...
True. I can imagine a kafkaic scene with the reborn person talking to some official, telling them that they're dead and they can't be of any help, despite them standing right in front of them.
Realistically, Netflix documentary, lots of interviews, newspaper articles, sharing by facebook uncles. If that person is religious, either a following or a statement about seeing the light.
If they've been dead for a while then the body is going to be quite decayed so that unfortunate person would end up dying again immediately.
Unless you're suggesting this thing that came to life is no longer human. So in that case decayed body/flesh, missing organs/bodyparts, etc. no longer prevent it from "life". But I'd argue that isn't a human coming back to life, more like a corpse transforming into something else.
A few months ago, we had a question about what would happen if necromancy was possible and an undead was called as a court witness. I gave a rather fun-to-write, tongue-in-cheek answer, which might be germane to your question too. Here's just a snippet:
So now we come back to zombies. Would a jury be able to set aside their shock, horror, and awe about a zombie in court that they could focus on being the finder of fact? If a zombie says they’re an eye-witness to a mugging, would their lack of actual eyeballs confuse the jury? Even more confusing would be a zombie that is testifying as an expert witness. Does their subject matter need to be recent? What if the case needs an expert on 17th Century Parisian fashion and the undead is from that era and worked in haute couture? Are there no fashion historians who could provide similar expert opinions?
Depends. Once you're dead and everything stops working, coming back means dealing with decomposition and a shitton of toxins. Can the system deal with it naturally? What's the first stuff to go during decay and can the body do without them?
As others have stated, you're still going to have to define dead, and you're going to have to define the question of what happens. I suspect you may not actually have any specifications for either and are just having fun thinking up and about random shit (that's not a dig; I share this hobby).
But for the sake of further discussion, let's add a few more specific (but non-limiting) questions just to help the discussion along.
I'm going to exclude cases where they're already deeply buried or cremated because the obvious answer is "stay there" with the exception of a purely magic related situation where their body just spontaneously recorporeates somewhere? What would be the social consequences to that, how would people react, and what would happen to any property they left behind? This actually raises a lot of other questions related to the social dynamics such as:
how would the people immediately around them react.
what proof would people need to believe it?
are they still on the hook for their student and medical debt
would it likely start a new religion and how would the existing religions feel about it from most to least happy?
There's also some physical questions such as how much skin, muscle, brain, and other organ breakdown would have occurred and which part would have the most damage.
There's questions about whether or not they're likely to have experienced something spiritual (including what we DO know about near-death experiences like the commonality of a peaceful feeling or spiritual experiences.
I gave no great answers to any of these and additionally encourage others to ask similar hypothetical details to ask about.
Death is rather difficult to define precisely. If you define it as "the cessation of consciousness," then you die every night. Every sleep cycle has some portions of minimal brain activity. There's nobody home for these periods.
It would no longer be the world-view destroying event that it would have have been 100 years ago. The moment someone came up with the idea of a matter-energy transporter, we had the idea of how someone could come back from the dead. Today we know exactly how it would be done - we just lack the technology.