The JW org is first and foremost a Bible quoting religion. They imagine that by quoting scriptures and examples from the Bible it is the key to answering every problem.
I agree NK this is dangerous and foolish.
The 'sister' in the vignette is conditioned to expect the sort of comfort recommended (Biblical examples) but in the real world grief and loss is not healed by unqualified help from spiritual leaders of the congregation. As you say, they need professional treatment.
The reluctance to do this on the part of the org. I think, is because they imagine "scripture quoting" is a panacea and secondly the GB will not relinquish their total control over a member to outsiders, even if this means they do not get the right help and suffer more as a consequence.
I do hope the lack of enthusiasm for the JW org's prescription was a general indicator for lack of loyalty to the heartless, self interested governing body.