I mean nobody ever names an era of a team after the GM at the time. We call it the Jim Mora era, not the Jim Finks era.
Regardless, we don't know if it was Payton or Loomis really pushing for Brees or who made the final decision. But, considering that Payton was a young first time HC with no experience or history making personnel decisions, it seems likely Loomis at least made the final call on what at the time was a large contract and a lot of money from Mr. Benson.
But sure, Payton should get the vast majority of the credit. But Loomis should also get credit for hiring Payton, letting him do the job the way he wanted to without interference from the GM, and doing what was necessary to give Payton the players he wanted.
Anyway, as I said, I would prefer if they moved on by moving Loomis to a different role or letting him go, but I can see why one bad head coach hire and few years of mediocrity, might not be enough to Gayle Benson to fire or move Loomis out of the GM role. I also don't think it's a disaster if he stays since he's a solid GM, but if he stays he needs to hire a head coach that is good at talent evaluation so he can turn most of the draft decisions over to him.