He is talking simplistically regarding hands to enhance a point he was making without being very careful. He should have said that its possible some atoms in each hand to not be from the same star explosion and most likely the fraction of that is the same in both hands.
The idea is that you have all kinds of things in interstellar space. You can have mostly hydrogen, then some nebula rich in higher elements result of a supernova, then nearby (many light years) another supernova remnant nebula, maybe a star like the future of our sun that has expanded and released most of its hydrogen outer layers or even original unused hydrogen that never "lived" inside stars etc.
Basically imagine the universe as rich in hydrogen originally , then forming stars, most very big, living much less than 1 billion years then exploding doing all kinds of things depending on their masses, then the resulting galaxy content mixed continuously with the old hydrogen and the products of the explosions and so on until new generation of stars are formed that have progressively with each generation elevated concentrations of higher elements in them (metal rich stars) etc. You end up after several billion years having a system that has almost everything, lots of hydrogen either recycled (like our sun will do )or unused yet plus nebulae expanding in all directions carrying higher elements and all kinds of stars in between. Imagine all these things over time mixing, colliding (gravitationally interacting) with each other "diffusing" their content all around until conditions for a new star to be formed are favorable and recollapse of that local matter starts, formation of solar systems with rocky planets if lots of higher elements exist etc.
Look at a picture of a supernova explosion that happened say 1000 years ago and you will see the gas having traveled a lot since then. Imagine that going on for many thousands of years until it hits another nebula doing the same from another direction or until it hits a hydrogen rich area and interacts with it causing eventually Jeans instabilities (http://en.wikipedia.org/wiki/Jeans_instability
) due to this mixing and starting new stars at some points of all this chaos.
Imagine the universe as recycling hydrogen in stars that is not fused and the higher elements produced in earlier supernovas from fusion and eventually rebuilding stars and solar systems with the mixed material only to repeat that in the future again with newly recycled matter after each system dies and either explodes or expands after living many billion years as solar system (as in our type of system say) or binary stars etc. In the process creating also black holes, neutron stars, white dwarfs or very very long lived stars, new nebulae etc. Its like a garden or forest that goes on recycling itself with all kinds of plants born each year from the recycling or prior ones. At a random point you have all kinds of plants and trees, the outcome of all the mixing of past processes in that garden. You expect say eg a tomato plant to be using some atoms that belonged before in a pine tree or an apple tree or an olive tree or even a rose plant, a strawberry, even a dead animal or its waste products etc.
We can try to see what has happened by using long half life isotopes to figure out how old some material is. But i certainly do not expect that there are areas on earth that have dramatically different isotopic ratios indicating origin of say Uranium from 2 different supernovas. Thats probably because the most likely origin of our system is recycling to form a new solar system from the mixing of an old supernova explosion material with other hydrogen rich nebula or basically old diffused interstellar gas (mostly hydrogen). So some Hydrogen is from one explosion and some hydrogen was from another or from the background gas. So in terms of Hydrogen there may be decent mixing from different older stars content or nebuale . In terms of the higher elements not so safe to think so, maybe most are still from the same old supernova but all is possible why not. ( Eg imagine we have content A original from one supernova mixed with content B from another or C just hydrogen gas region etc). After the mixing local conditions that lead to star formation develop.
Imagine the expanding gas from a supernova after enough time has lost its kinetic energy and has mixed well with whatever it found on its path and after a while the resulting mix may give new systems.
Thats a crude idea of what can be going on.
PS: In terms of our bodies most of it by mass is Oxygen (way more than any other element, so it better be from the same supernova typically). So we are called carbon life forms but its really Oxygen by mass and carbon is in fact far less but of course existing in all organic molecules.