ID does not just claim that "God designed science." ID claims that "God designed science" but that the "science" which God "designed" is not always adequate to explain the results which we observe. No, ID claims that that the quarterback can't always throw the ball accurately by himself.
I don't think this explanation is quite correct. ID seems to say the following:
1. The universe and its laws, as normally conceived, were created/designed by an intelligence
2. Science would therefore have come from this intelligence because science/scientific knowledge evolved from human culture
3. Science would not necessarily explain all events if it limited its explanations to always fitting into a naturalistic methodology
ID strictly speaking doesn't say that the above was done by a God or gods. Although it usually seems to equate to a god with attributes like the Christian god. They would perhaps say that the "I" in ID could be one of the following:
1. The "I" in ID could be a God or,
2. The "I" in ID could be "gods" or,
3. The "I" in ID could be very powerful Intelligent agents that have technology or abilities far beyond our own but is neither a God or gods
They seem to be saying something like some statements of nature can be made but not understood within a naturalistic framework because this framework is incomplete. I'm not sure how practically or possibly this statement is since without being able to do empirical experiments on it, how could one establish it as a viable structure of knowledge. If you can do experiments on it, than it just seems like another part of the naturalistic methodology/explanation structure