There are three ways to attach a chimney cap. First is to bolt it tight to the chimney tile that is protruding above the crown as the majority of them do. 
The next way is to use brackets to attach the cap to the chimney crown itself. We do this with concrete anchors to prevent the cap from blowing off during windy weather.

The last and least preferred method is to use metal slip in legs to attach the chimney cap. This mounting method is rarely successful and we refuse to attach a cap this way. This is the easiest way for sweeps to attach them when the flue tile is flush with the top which may explain their prevalence. As a chimney becomes coated with creosote the cap legs stick in the chimney and stay put. But when the chimney is swept properly the bond holding the legs in the chimney is broken and if the legs are just put back like they were chances are great it will blow off when a strong wind comes. Under these conditions we mount the cap with brackets to the crown to ensure it stays put.