I'd need to look details up, but in general also on DNA you basically need a specific anchor where replication can start, and this just doesn't happen anywhere. The body should also get rid of the exogenous DNA, since it will be recognized as foreign.
I guess there's a chance that it could get integrated randomly, but that chance should be really small, and even then the cells will probably be killed in the long run by T-killer cells.
EDIT: The mechanism is so that in general all cells will represent to the outside a digest what's inside of them (not all at once, always a random selection). If anything unusual is detected, what doesn't belong to the body (e.g. during a virus infection), then the cell will be killed. This applies to proteins transcribed from the DNA (well, from the RNA translated from the DNA), and not DNA itself though, but since we need protein for anything to happen, this should still apply.
I guess there's a chance that it could get integrated randomly, but that chance should be really small, and even then the cells will probably be killed in the long run by T-killer cells.
EDIT: The mechanism is so that in general all cells will represent to the outside a digest what's inside of them (not all at once, always a random selection). If anything unusual is detected, what doesn't belong to the body (e.g. during a virus infection), then the cell will be killed. This applies to proteins transcribed from the DNA (well, from the RNA translated from the DNA), and not DNA itself though, but since we need protein for anything to happen, this should still apply.