This is sounding very 'icky' to me and a reason I would turn my privacy settings on. The issue is that people don't TRUST that if they send stuff to leadership that it will eventually get to the lowly member of the church. This is very often the case, so they try and bypass any leadership level communications and send it directly.
A stake and ward should have a plan for communication - Typically, by role, clerks and exec sec's are/should be 'trusted' members to send these communications. This will guarantee that leadership has 'signed off' on the communication and that as a 'lowly member' I have trust that the message has been 'vetted'
In my stake we consolidated all communication into a weekly message sent out - everyone got very used to the idea that this was the message - there were exceptions, but they were typically only SP level. - Wards were free to communicate how they want.
“A long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom.”
― Thomas Paine, Common Sense