I can see both sides. The grief of bereavement varies a lot, from completely devastating to an acceptable sadness. I grieved far less when my father died than when my mother died, for instance. The reasons for that are complex and even I probably couldn't explain them, that's just the way it was. It also depends on the manner of death, some are more traumatic than others.
How does a company measure grief? How do they separate the real grief from someone merely perhaps taking advantage? There has to be some parameters. Some people would appreciate getting back to work as a distraction and returning to the comfort of routine. I think it's a really grey area and I can understand a company not being too happy to pay for a lot of time off. Mind you, I think 3 days is probably too little in many cases. Bereavement can be extremely debilitating, but if it is, I think people need see a doctor or counselor and take sick leave, and yes, employers do need to be as supportive as possible. Some of those cases in the link are plain wrong.
In the beginning there was nothing, and then it exploded.