I agree, while the company wants to promote customer service, they reserve the right as a private company to do this (it's in the fine print). I think SWA should create a clear (not rigid, but clear) dress code policy on the web site so that people know that if they show up topless or whatever they define as inappropriate, that they may be denied to fly on the airline (no shirt, no shoes, no service).
Otherwise, where do you draw the line? Should they allow completely nude people on the plane and would it be hygenic? Here's a few rules from the Carriage Contract (online):
"Comfort and Safety - Carrier may refuse to transport or remove from the aircraft at any
point any passenger in the following categories as may be necessary for the comfort or
safety of such passenger or other passengers:
(1) Persons whose conduct is or has been known to be disorderly, abusive, offensive,
threatening, intimidating, or violent, or whose clothing is lewd, obscene, or patently
offensive;
Persons who appear to be intoxicated or under the influence of drugs;"
http://www.southwest.com/travel_center/coc.pdf
They had the right to do it. If you're going to travel with a private company, either cooperate with them or fly someone else. OR write an angry letter and get that canned response.