UML is a modeling language for object-oriented systems,
whereas COMET is a design methodology for developing OO systems
(particularly concurrent, distributed, real-time ones).  COMET,
like other design methodologies (such as USDP/RUP) allows for
the use of UML during design phases of the engineering project.
Although UML can be used in a COMET-using project, it does not
seem to be required, nor does there seem to be any particular
advantage to using them hand-in-hand.  The presentation seems
to use UML as a catalyst for conversation rather than
employing any implication that UML is a required or preferred
tool for implementing the COMET design methodology.