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Jay: I'm a Campbell with 3 kilts - MacBeth, Cummings and Black Watch. 
I do not own a Campbell tartan ad I am not all that interested right now.
Interestingly, according to the STA site. the Black Watch is the same sett as Campbell, but in a darker shade!

On the wider point of clan chiefs and clan tartans, the 13th Duke of Argyll only recognizes the (Ancient) Campbell tartan as a Campell tartan (apart from one or two others such as Campbell of Breadalbane, C of Loudoun and C of Cawdor belonging to different branches).

The fact that a clan chief recognizes a particular tartan or tartans as the tartan(s) of his clan is quite different from an assertion that only someone of his clan has a right to use them (whether as a tie, a blanket, a shirt or pyjama pattern or a kilt).

The former assertion means that those tartans, and those only, can rightly be called the tartans of that clan. Consequently, no user or wearer would have any basis for considering that a different tartan from those was the clan tartan.

The latter claim, if it were ever to be made, could only have substance if it were backed up by copyright restrictions, in which case the general public would not be able to get its hands on the tartan in any case.

Of course, there are a number of matters of etiquette that will govern whether, how far, when and in what situations if any, such other tartans might be used or worn ... as many other threads will indicate!