In an interview with PC Gamer, Howard said that it was Bethesda who approached Obsidian with an offer to make the game after Fallout 3:
When we started working on New Vegas, we had just finished Fallout 3. We knew we would be working on Skyrim. We know the guys from Obsidian well — we love their work — so we approached them and said: „Hey, would you like to do this? We see an opportunity to create something new after Fallout 3“.
When asked about the fact that players sometimes like New Vegas more than Fallout 3 or 4, Howard replied:
That's what we asked them to do, and they did an incredible job.
Rumors of a conflict arose because of a bonus in the contract: Obsidian could receive a large payout if New Vegas scored 85 points on Metacritic, but the game received 84 points, and the bonus was not paid.