While it is interesting to think about how intractible problems for the poor can be minor issues to the rich, and how that affects one's decision to be euthanized, ultimately, it isn't the right to choose to die that should be taken away.
There are real cases where euthanasia is a compassionate choice. Outlawing it just forces people to suffer needlessly.
The authors appeal that the government is a uncaring cost optimizer pushing death on the poor misses (or misrepresents) the point. The issue isn't euthanasia, it is that living conditions of the poor are untenable. The solution shouldn't be to force them to live a long life through government enforced misery, should it?