According to this answer, Genesis is not to be taken literally by the Roman Catholic church due to the scientific evidence contradicting it. In this view, what is the basis of the original sin?
The basis is that we were in a perpetual state of grace and "did something" that opposed God's commands, which took us out of that state of grace.
The rest is just footnotes.
Edit: In response to David's question in comments, I'm going to flesh this out a bit.
For Catholics, we subscribe to the notion that much of the early Old Testament is not a literal "this happened, then that happened" scenario. Genesis is a prime example of where we believe the specifics of the creation stories and the "Fall" are irrelevant to the Theology that is being expressed within.
So, that being said, we really don't concern ourselves with the specifics, other than to say we strongly doubt there was a literal tree, a literal apple, etc. The Theology being expressed within, however, is a different matter. That Theology suggests that there was a time immediately following our creation when Humanity lived in an idyllic state and were close to God (in the "I can see God face-to-face" kind of close). Faith was not a requirement, because we could see and interact with God. In other words, belief was not in question.
Flash forward to some point after creation. We voluntarily chose evil over good. The specifics of what we chose and how we chose it don't really matter (to Catholics). The "take away" is that we did something that God asked us not to do. This "something" was so fundamental and so "essence-changing" that it was simply impossible for us to live in that idyllic state of being any longer. We suddenly found ourselves in a less-than-idyllic state.
For Catholics, that is the essence of Original Sin.
[Edit: Since citations were requested...]
At the first link, the entire article is good, but the section titled "Nature of original sin" probably answers the question directly.
The second link: Take a look at "How to read the account of the Fall"