I think you are arguing on two different levels. I'm a professor biologist and though it strikes me as a pretty indirect mechanism (arguing the effect size could be small), I see some merit to the commenter's idea.
The current hypothesis is that humans have a longer lifespan because having living grandparents conferred a survival advantage over having only parents. Arguing that elderly relatives confer a disadvantage would seem to directly contradict that hypothesis, unless somehow grandparents were beneficial but great grandparents were not.
