When someone else sends me an appointment to Outlook 2003 and I accept it by
clicking on Accept in the email, Outlook actually declines the invitation
from that person and creates exactly the same appointment but with me as the
originator and sends it to all of the people who were invited to the orginal
appointment.

Example: Annie sends a meeting invitation to Bertie, Carol, Dennis and me.  
When I accept this invitation in Outlook 2003, the result is that Annie sees
that I have rejected the invitation, and Annie, Bertie, Carol and Dennis all
get the same invitation but with me as the originator.