I don't think that the vast majority of atheists have ever claimed that on the surface, the entire Bible is false. I think I can sum it up very well thusly: the movie Titanic (Leonardo deCaprio) is fiction. Imagine a world, 2000 years from now, where someone claims that all the details of that movie really happened - what Rose's life was like, etc., and then uses the finding of the ship pieces at the bottom of the ocean as a basis to support that truth.
Many of the stories in the Bible are parables. And, for centuries, they were recognized as such. If you research historical writing of the era the Bible was penned, you'll see that much of it was parables. And, many of the stories had been passed down, pre-dating Christianity. E.g., Epic of Gilgamesh.
Let's say for a moment that God created the Big Bang. There's no way the Bible could describe this - stars weren't even understood back then. And, how about talking about observing the universe via red shifted galaxies. Red shift? 2000 years ago, there was no concept of electromagnetic radiation. Today, there is nothing clearly stated in the Bible that can be directly interpreted today as describing any scientific phenomenon that wasn't understood back then. You'd think that at some point in the past 2000 years, we'd make a scientific discovery and realize, "OHHHhhhhh, so that's what it's talking about."
Further, the Bible describes space-time relationships in such a manner that Heaven is clearly "up." It's not in another plane of existence. Ancient drawings make it fairly clear that hell was inside Earth, and Heaven was where the stars are - that was the understanding of the time; the Bible caters to that understanding. Yet, we can see "up" with our telescopes. In fact, I'm often left wondering why the literal interpretation completely ignores this. In fact, literally taken, the universe is layered - which we know is not true, but theologians 1000 years ago did not know this. In fact, many early theologians believed in a flat Earth, because to believe otherwise caused some major problems in knowing where Heaven was.