When creating a new Story record, and attaching a Project by using the reference lookup field Project, few Project records are returned (fewer than expected)

M,N,O

The project field of the rm_story table as a unique Reference qualifier: javascript:ScrumSecurityManager.getStoryDotProject(current);

This reference qualifier, defined in the ScrumSecurityManager Script Include eventually leads back to the Agile2SecurityManager Script Include where getStoryDotProject is defined as:

getStoryDotProject: function(story){
   var projectId;
   var qualifier = 'sys_class_nameIN'+PPMRoleClassMapper.getClasses('project', gs.getUser());
   if(JSUtil.notNil(story.demand)){
      projectId = story.demand.project + '';
      qualifier = 'sys_idIN'+projectId;
   }
   qualifier += '^execution_typeNOT INwaterfall';
   return qualifier;
},

In short, for new Story records (where there are no values to check), the method compiles a list of Project records that are NOT using the Execution type Waterfall. It will only display a list of Projects which are Agile or Hybrid.

Only projects which are Agile specific may be included in Stories (agile development).

This is the expected behavior. You could always change the Execution type of your Project to Agile or Hybrid in order to utilize a Project into a Story