I couldn't have explained the notion of rituals better myself, and I have a degree in macrobiology. I think "death ritual" may be the best way to describe what Dr. Bekoff wrote about.
I think what most scientists are opposed to is *gratuitous* anthropomorphism. I didn't take any courses with Dr. Bekoff, but his colleague at CU, Dr. David Chiszar, really made a point of discussing this topic. And rightly so. Gratuitous anthropomorphism is the practice of taking an animal behavior and attributing human motivations to it at a prima fascie level. This is a problem because it keeps from digging deeper and actually doing any meaningful investigation. HOWEVER, and any scientist will likely agree, animals and humans share most of the same prime motivators, so you can rule-out a common motivator for a similar behavior.
Gratuitous anthropomorphism would say that the magpies held a "funeral" to bid their fallen comrade farewell and brought grass for it to thrive in a corvid afterlife.
Scientific inquiry would try to distinguish coincidental behaviors from those that the animals behaved in as a direct result of encountering a non-responsive comrade. This is much different from taking a hardline that animals can't experience emotional responses or do anything for reasons that would remotely resemble human motivations.
Based on the abstract that the Reg presents, it sounds like bringing grass to the corpse was a deliberate act and not a coincidence. I'm guessing Dr. Bekoff didn't observe them attempting to eat their dead comrade, and like most animals, birds explore their world with their face-- their beaks are their primary means of manipulating objects in their environment. Their "death ritual" is quite likely nothing more than them attempting to elicit a response from a fallen comrade before abandoning it as dead. That's a little something that humans would consider "closure", and we do similar things for similar reasons. It keeps us from abandoning our friends and offspring just because they're taking a nap or took a hard knock on the noggin and are out-cold for a few moments, and puts us in a place we can just move on with things and stop being concerned with the welfare of those no longer with us when they are really deceased.
I'm curious as to the grass bit. I highly doubt it would be an offering to the dead. The most likely motivators would seem to be either providing something to tempt the fallen into responsiveness, or maybe the odor of plucked grass has an effect similar to smelling salts on corvids? Maybe it's just a bizarre habit that one magpie learned by observing an eccentric magpie long ago. Further research would be required and hopefully will be done because that's a pretty interesting behavior to get to the bottom of.