That is about right.
One notion is that certain things that have happened in evolution required God to have intervened to make them possible. There are other views too that do not precisely require intervention. However, in addition to this claim (which might be correct) is the presumption that we can scientifically show this to be true. That presumption motivates a lot of claims from evidence that turn out to be false.
God certainly could have intervened. This does not violate science, because science is silent about God. However, if He did intervene, given what we have seen in nature, and how science works, we do not expect to determine how. That is just as it is in all areas of life. God providentially governs all things, including evolution, even though we do not know the precise details of how He governs all things.
This goes against the first part of your statement.
And on this you are on much more solid theological and philosophical ground than one of the leading lights of the ID movement.
The problem is that you have to be able to demonstrate something scientifically for it to be part of science class. And historically, ID has always been about getting into science class. Hopefully that will change in the future, especially as they become more engaged with theology, and more upfront about their religious motivations. ID does not have to be about the Dover Trial and the Kansas Hearings, but they are going to have to evolve.