In the case of the Halfling his ability provides an exception to the requirement of not being seen before you can attempt to hide.
Why? How does it provide that exception? Reading the single sentence on page 28, PHB,
Naturally Stealthy: You can attempt to hide even when you are obscured only by a creature that is at least one size larger than you.
Where in that sentence does it allow the halfling to hide from a foe who already sees him? I'm not trying to be obtuse, and I'm not trying to nerf this rogue. I'm just trying to maintain minimum believability.
It's much like the box trick someone cited above. To allow that strains my ability to suspend disbelief. Yes, I know that wizards can bend the fabric of reality, and yes, I know that a halfling rogue should be super ultra slick fast stealthy, but come on!
Another example I've used is, what if you and I were standing in a parking lot in full view of each other. I walk over to a car and duck down behind it. Am I out of sight? Yes. Do I get cover? Yes. Am I hidden? No.
Furthermore, in that sidebar on page 177 (thanks again for the correction), there's that sentence concerning invisibility.
An invisible creature can't be seen, so it can always try to hide.
That, to me, implies that you must be unseen in the first place in order to make a hide attempt.
I've read some good arguments pro and con in this thread, as well as some compromises. It sounds like I'll just have to DM rule it. I'll probably err on the side of the player, but I sure wish there was some official ruling on this that we could just cite and move on one way or the other.