On page 21 of the GHBI this is discussed. It says essentially that the ward welfare committee should become familiar with and utilize community resources. It further states that if a member uses government assistance the bishop should make sure he does not duplicate government assistance and that the member should be advised to disclose Church assistance in their attempt to receive government assistance.
I wonder if this change in attitude towards government assistance was caused by the realization that it simply wasn't possible for the church to address all the needs of their distressed members. I wonder if the increase in membership in third world countries has contributed to this realization.