It says nothing about the presence of designers in the process, however: and we know from human experience that designers can and do influence how species change. Note, however, that you're simply assuming that common descent is an absolute fact. It may in fact be true (or not) -- but unless you want to theorize that there's only one possible way for life to come about, common descent is not a biological requirement.
ID would certainly not have such a requirement.
Neither does evolution require such a thing -- it could have just turned out that way. Anyway, common descent is still not an argument against design. Perhaps it's a poor analogy, but pretty much all of my very numerous C++ programs originated from the first "hello world" program I wrote 15+ years ago. Why? Because it's easier to modify what I've already done, than to start from scratch every time.
Where I believe we disagree is in whether this is a scientific theory or not.
Well, given that we both agree that intelligent designers not only can, but quite often do intervene in the development of species, I fail to see why it is "scientific" to simply exclude the possibility when the topic turns to evolution.
It doesn't have to be something that has actually been observed. (Such as my example of an organism with something other than nucleic acids as its genetic material which has never been observed.) If there's no way to show that an idea is false, it is not science.
The only "false" idea in your previous example would have been that DNA is the only way to pass genetic information. However, it is pointless to provide "falsifiable tests" for things we already know to be true -- such as the fact that intelligent designers have influenced the development on species on Earth.
My argument is not designed to argue against ID. It is designed to show that evolution is potentially falsifiable. Would you not conclude that the theory of evolution is false if you saw an organism that has silicon oxides as its genetic material. Such an observation would be fatal to evolution. We don't know for sure that such an organism will never be found. Evolution predicts that such a creature will never be seen, though. Therefore evolution is falsifiable. I imply nothing about ID in any of this. I do ask for a similar example using ID as a starting point. Namely, give me an observation that, if actually seen, would render ID false.