I think its very farfetched to believe that the committee deliberately gives UNC a tough road as punishment, or because they don't like UNC or whatever. They do however, clearly orchestrate specific matchups in the 2nd round, sweet 16, etc. that will allow them to better market their product, which I have no problem with. In years that Kentucky/Kansas/MSU/(anyone else they can get a good UNC storyline with) is good, that doesn't benefit UNC as they will likely be put in the same path as those teams. However, if Kentucky were reeling right now, and Ulis had just torn his ACL - the committee still would have put Kentucky in UNC's bracket and we'd be happy that they set up matchups because in this case it would have benefited us.
That said, Duke does tend to get fairly easy draws year in and year out, and can be said to get a seed or two higher than they probably deserve fairly frequently as well. Look at their rankings entering the final weeks in past years, and the rankings of the teams that are in their regions. I'm not saying it's drastic - that they earn a 10 seed but get gifted a 2 seed and play mid-majors throughout - but they do frequently get seeded a spot or two ahead of their rankings and get some favorably ranked teams in their path as well. I think it's hard to say it's a coincidence that this happens regularly, and there are Duke people on the committee. I'm not saying this is a conspiracy, which is defined as "a secret plan by a group to do something unlawful or harmful."- because I don't think its a secret, and I don't think it's unlawful or harmful - it's just giving the benefit of the doubt, or a push in the right direction, to a person(s)' team they have ties to.