I didn't find it paper thin at all. It's just not all there; that's the charm. Sure, I'm a lowly letter carrier for some dude in Primm but when you look back on the story especially after beating it.
It's hard to explain. The story just feels too large-scale and impersonal. Disjointed at times, leaving me with no idea of what to do next. I just started doing missions for the NCR, because I had no clear notion of what to do. I can think of way worse examples than this, but the way I see it, the game is most enjoyable when you're doing a chain of quests for one faction, rather than trying to piece together the over-arching plot. They could've been more creative with some of the quests, but that's a minor thing by comparison, not really something I'm concerned about.
I think that, above all, the story could've been more exciting if they'd left out the platinum chip bit, the whole deal with Mr. House and all. They could've focused on making the other stuff more interesting.
As far as the story being lacking and not personal? It starts by you getting shot in the head, and going after the person responsible. Oh sure, later on, you find out you have been thrown into the middle of this multi-sided confrontation. At least there is no clear cut "good" and "evil" faction.
You get shot in the head, and ... that's about as personal as the story gets. The rest of the time, at least in my experience, you spend preparing one faction or another for war. Or trying to figure out why you can't just throw the platinum chip away.
That damn platinum chip, now I can't get over it!
Worst of all, though?
I mean, the one thing that would instantly have made this game twice as good? The one thing they left out, that just begs to be in the game?
Me, in Veronicas pants. Or ... Scribe robes. I guess.
Edit: I was just about to assassinate Papa Khan. I was in his room, stealthed, but didn't have a silenced weapon that could take him out in one shot, being more partial to high tech weapons of mass destructions ... but I figured, I'd come that far, so there had to be some way I could take him out in his sleep ... That was when I noticed the leftover plasma grenades in my inventory. The rest sort of followed from there.