You're right. They did.
But that doesn't mean it's in the style of a Bethesda game, does it?
Is Quake like that? Is Dishonored like that? Is Brink?
All those are Bethesda games.

Well fallout 3 was made by Bethesda game studios.
Quake, dishonored and Brink were not.
So was fallout 3 in the "style" of a bethesda game?
When you use a game as a template, you are modding. New Vegas is a big mod for Fallout 3 so yeah, it would have been silly to work so much on a mod and not improve the original. However, they did screw up the open world feeling, their game has much less incentives to explore.
Is not every game just a "mod" of the orginal in some form?
Also, explore what exactly? What incentives do you need?
Fallout was never about exploring, it was about Story.
And almost every location in NV has a story.