In ZZ Packer's book of short stories "Drinking Coffee Elsewhere", the
first story is called "Brownies."  There is a reference to Mennonites
that claims "They're these people who, if you ask them do a favor,
like paint your porch or something, they have to do it.  It's in their
rules."

Is this true?  I'm looking for a credible authority to state whether
this is true, exaggerated, or false.  The history of such a tradition
would be a nice benefit

Perhaps this refers to the Mennonite tradition of "mutual aid."
Mennonites are noted for being helpful to those who are in need:

"...a historical emphasis on mutual aid that goes back to the
sixteenth-century beginnings of the Anabaptist movement. 'Anabaptism'
was the name given by contemporary critics to communities which grew
up around a group of reformers emerging out of the Protestant
Reformation - a movement that charted a course distinct from either
Lutheran or Calvinist understandings of theology, community, and
lifestyle.

Anabaptist leaders understood that the Christian church ought be a
covenanting community in which members would follow the example of
Christ in their daily living and support each other, as well as those
in need around them, in all aspects of their lives. They believed that
they were not only obliged but privileged to share their gifts in
response to God?s supreme gift of love and reconciliation through
Christ."

http://www.mennofoundation.ca/mfc1_4.html

Some examples of mutual aid:

http://www.mhsc.ca/index.asp?content=http://www.mhsc.ca/mennos/tservice.html

Now a days there are several divisions in the Menonite faith so my
guess is free loaders don't get their requests granted very often, but
persons in real need with a good attitude are likely to get help. 
Neil