We probably can keep a heart alive outside of body, through artificial means, for minutes, maybe hours - and I mean keep it functioning, not just chilling it to slow its death. It's plausible we'll learn to be able to keep it alive for days, months, years, decades. At which point we could say that the "supporting infrastructure" of the rest of a human body isn't necessary for the heart to be independently alive?
What if we do it all on the Moon, or Mars? How does Gaia feel about it? We already know that it's theoretically possible, if not yet achievable in practice, to create artificial environments capable of supporting human life indefinitely - or, on a long enough timescale, bootstrap an independent, self-sufficient biosphere. The two are, in the limit, the same thing anyway.
Or are we going to argue that human technology is, by extension through causality, a part of life on Earth, and therefore a part of Gaia itself? Is Gaia in all of us, and will it persist after Earth dies if humanity is still around somewhere else?
All in all, I suppose the correct definitions of terms are the ones that are most useful in a given context :). "Categories were made for man, not man for the categories", and all that.