Every lootable item in Pete's arena can be reached by using the lift to gain that height, and then simply walking off to either side. Before taking on Pete as a raid boss, the lift is always active, so one can hit these boxes on their way to the two chests further on. After taking on Pete as a raid boss, the lift is only active after a fight, but can still be used to reach these areas without using grenades. If you want to use these areas strategically during the fight against Pete, then grenade jumping is necessary, but having made that climb myself, I'm almost certain that was not intentional.
Let's make a list of places with lootable objects and locations in BL2 that require grenade jumps to reach. We will assume for the sake of this hypothesis that this implies that these areas were intended by the developers for players to be able to reach. If there is one that exists which is not ever reachable without grenade jumping, this will imply that grenade jumping was an intended game mechanic. (This also assumes that the lootable objects in the world were vetted for this by the developers and not, say, randomly/prodecurally placed). In TPS, for example, there are some lockers that I have not yet found a way to reach by any means, but let's simplify this by sticking to BL2 for now.
I still posit that the red chest over the third Eridium Pumping Station in Arid Nexus Badlands cannot be reached without grenade jumping. Has anyone made it there without? I'm still trying.
Are there any other examples of lootable objects that can only be reached by grenade jumping?
edit - I just thought of one: the red chest in Hunter's Grotto that you must reach from the Ardorton Station pass through... I'm fairly certain that there's no clearing that gap without grenade (or rocket) jumping.