The many changes of SCO's claims throughout this debate show that the former of the two options you have listed applies, that is, they do not have a case at all and merely want to make quick cash.
I can't remember all of their claims anymore, but I do remember that they have initially stated that Linux contains a few
million lines of code stolen from System V. After much pressure, they have finally pointed out a couple of files they thought was theirs (namely parts of bpf - Berkeley Packet Filter, and I think an ancient malloc function written by Dennis Ritchie or something like that), but they were all proven to be legitimate (because they came from BSD or legacy Unix from the early 70s).
Then they pointed at a bunch of (trivial) files containing mostly error handling and character classification macros (
errno and ctype in case you're familiar with them), but their ``proof'' of them having the same values (in case of the rerno stuff) and structure (in case of the function-like ctype macros) could be traced to the Open Group specification and common sense.
Eventually, they have stopped claiming code theft completely. Now (unless they've changed course again and I didn't notice) they complain in court about the fact that Linux looks and feels a lot like System V, i.e. they claim plagiarism of the ideas and concepts behind all that.
I think you may find better timelines at
www.groklaw.net
Some people also believe that SCO is doing this on behalf of Microsoft, but regardless of such conspiracy theories surrounding the real motivations of SCO, the fact remains that SCO's ownership claims themselves are plain bogus.