It's more like a math problem which then leads to a sync problem. Here's the tl;dr version: I have an iPad with 5GB of free space, and I cannot add a 1.8GB movie to it, as iTunes eventually tells me it needs another 526MB of space in order to do so.
During the attempted sync of this movie, iTunes displays some horridly bad math skills; just watch the video to see.
Here's the video at its full size (1164x1056).
I have no idea how to resolve this, short of restoring the iPad, which I'd rather not do. (I've already unsynced and resynced everything, in an attempt to straighten out the math, but to no avail.)