There are a wide variety of reasons why you may be denied boarding. I described some of the alleged security reasons here with references: Physical appearance and clothing, do they affect the passenger's chances of getting on the plane?Physical appearance and clothing, do they affect the passenger's chances of getting on the plane?
In the example in question, the reason was not security (or a pretence at security), it was (allegedly) decency. From the article:
The airline’s policy states that they have the right to remove anyone from a flight ‘whose clothing is lewd, obscene, or patently offensive’.
Personally I don't think the clothing is 'lewd', 'obscene' or 'patently offensive', but it's not up to me. The airline in essence has the right to deny boarding for any reason; if you ask on avation.se they will tell you the pilot will make the final call. I would expect that if you flew with an Iranian carrier, the standards they would apply would differ substantially from (e.g.) a Swedish carrier. I think your quest for 'definitive examples' is not going to be fruitful, as this is a judgment call. However, the link above will take you to some ridiculous decisions.