of the 20 or so stove shops/installers I spoke with on the matter, none felt it was important if you burned truly seasoned wood and didn't smolder your fires.
Wonder, were they talking about a brick chimney WITH clay tile, or just naked unlined brick, as the OP has?
According to hearth.com, "If the chimney is not lined with clay tile... the liner must be insulated..."
My understanding is that if a masonry chimney does not meet the NFPA 211 standard, and one without a tile would not, then insulation is required to meet code.
Certainly many installers would not worry about meeting code, but I doubt it would be 20 out of 20.
The two sweeps I contacted (before doing the job myself) refused to install liners WITHOUT insulating... and that on an interior clay-lined flue! Personally, if I had a clay flue tile that was sized about right I'd skip the ss liner (and obviously the insulation) altogether, but the chances of that actually happening for anybody are pretty slim.