Is a Scheduled Reminder possible when something doesn't happen?
How about something like 


create a Group of all possible recipients of the reminder (X)
create a Smart Group of all those who did the Report (Y) 
create a Smart Group Z = X-Y (use 'Custom Search = Include/Exclude)
use Z as your 'target' in Scheduled Reminders


Alternatively 


create the Activity for every person who needs to do this
set the Activity to Scheduled
ensure that submitting the Report sets the Activity to Completed
set Reminder to go to all those that are still set as Scheduled