The paper shows that honeybees prefer sucrose (sugar) solution to a sucrose+morphine (pain reducing) solution. They find that injuring the bees (i.e., potentially causing pain) does not change the relative preference for sucrose vs. sucrose+morphine, but they do eat more overall when injured.
They indirectly conclude that because the bees do not seek a pain reliever they may not feel pain of the type that, for example, mammals do. This is not the same as the ability to detect noxious stimuli (nociception), which insects definitely have, it's more about the emotional/behavioral impact. They cite some evidence that morphine could potentially have similar pain-relieving effects in insects as it does in mammals due to changes in behavior caused by morphine, but of course the interpretation of their results depend very strongly on whether this is accurate or not.
ARC is the Australian govt's funding mechanism. They don't have any commercial ties to the results of research so there is no reason to have any skepticism particular to the funding source: everything has to be funded by someone.