Inside the body, your DNA is packed up into chromatin by wrapping around other proteins called histones, and then coiling those thicker strands around itself a few more times. One could make the argument that it's shape is different from isolated DNA, which doesn't have the histones, and is going to be much closer to a short string. However, trying to make the claim that this is a chemically distinct molecule is dubious at best, since the chemical structure and identity of the DNA molecule is unchanged.
There are, however, chemical modifications to the DNA itself that that may not get preserved in the extraction technique (but that really depends on your technique), and almost certainly won't be preserved if you need to amplify your sample to sequence it. The most common way is to put a methyl group (CH3) onto a particular part of the DNA molecule. Single-molecule sequencing techniques exist (but aren't comparably cheap to Illumina or SOLID sequencing yet) that would preserve this chemical structure.
Finally, Illumina sequencing (and probably SOLID too, though I'm not sure) involves adding on extra sequences at the end of your DNA fragments, which allow the sequencer to start it's work. I'd doubt if the patent covers this approach, so doing high-throughput genome sequencing like this ought to be fine, based on their "markedly different structure" standard, but who knows what the court would actually say.
But the appellate decision Friday rejected Judge Sweet’s reasoning, saying that since DNA is a chemical, the chemical structure is what matters and that “informational content is irrelevant to that fact.”
This paragraph is the most troubling to me. In the most obvious definition of the terms, the informational content and the chemical structure of DNA are two different ways of saying the same thing. It would be like saying, "the shape of the splotches of ink on this paper are what's being patented, and the informational content is irrelevant"
If you pretend the mRNA is object code, DNA is source code, and isolated DNA is reverse-engineered object code, you have a pretty solid metaphor. Oh, and comments = introns.
Either way, I was just trying to phrase it in terms familiar to programmers. No metaphor is perfect.
Update: After reconsidering, I take it back. Introns are important, especially intron boundaries. So, my new assertion: so long as your "compiler" translates "assembly with comments" into "assembly with the same comments intact," then I agree that your metaphor is apt.