It is not true that eukaryotic cells destroy all DNA that gets into the cells. For example, many of the genes encoded by primitive mitochondria, have, over the past billion years, transferred into the host genome (our own genome), a process that would be impossible if all cytoplasmic DNA was destroyed. And there is a bacterium (Agrobacterium tumefaciens - Monsanto really loves this guy) that induces a 'cancer,' of sorts, in plants by transferring some of its own DNA into the plant genome - but it does not actually enter or pierce the nuclear membrane. And all DNA viruses (eg, smallpox, polio, etc) that infect us must transfer their DNA outside the nucleus to either protein coats or 'budding' sites on the plasma membrane. So, no, not all DNA in the cytoplasm is destroyed and eukaryotes are capable of taking up DNA to integrate in the genome. Of course, as I've said before, the chances of this happening are almost vanishingly small since
1) DNA is a polar molecule and polar molecules can't really pass through the cellular membrane
2) Most DNA in the cytoplasm is destroyed by DNAses
3) Even in the nucleus, foreign DNA is very unlikely to be spliced into the genome.
But it has happened (see the mitochondria). And I was never comparing the process of transformation in bacteria to what we're talking about here - competent bacteria have specialized apparati to transfer plasmids which would be incredibly stupid to keep in multicellular organisms. And by the way, in biology at least, when you say "in the membrane," you mean "in the membrane," that is, embedded in the membrane. Cytoplasmic or intracellular would be more concise and far more accurate ways of saying what you meant, Idle Mind.
Oh, and swetha, the transfer of genes from mitochondria to the nucleus would, I think, be an excellent topic for a paper. It is extremely interesting, and puzzling, why another organism (the mitochondrion) would cede genetic control to us, the eukaryotes. I don't know if you are aware of this, but mitochondria - the organelles that make it possible for us to breathe oxygen and thus to be multicellular, were likely bacteria that were "eaten" by our eukaryotic ancestors about a billion years ago. Same with chloroplasts in plants.