Roles and Schduled jobs
Based on the information in SQL Server Agent Fixed Database Roles, it appears that non-sysadmin users must be a member of one of the following fixed database roles in msdb to utilize the SQL Agent:


SQLAgentUserRole
SQLAgentReaderRole
SQLAgentOperatorRole


Each of the above fixed database roles progressively allows more authority than the previous one, but with regards to being able to modify jobs, all three indicate that permissions are granted for owned jobs only.

The way I interpret the information in this post is, if you are not a member of the sysadmin fixed role, you only have the permissions to modify jobs that you own, whether that be an individual or a windows group.

You should be able to easily test this theory by creating two or more users, assigning them to one of the above fixed database roles (making sure they are not members of sysadmin), creating individual jobs under each user and then attempting to alter jobs not owned by that user.

I've included some information below about the permissions for each of fixed database roles mentioned above (highlighting mine).

SQLAgentUserRole Permissions


  SQLAgentUserRole is the least privileged of the SQL Server Agent fixed
  database roles. It has permissions on only operators, local jobs, and
  job schedules. Members of SQLAgentUserRole have permissions on only
  local jobs and job schedules that they own. They cannot use
  multiserver jobs (master and target server jobs), and they cannot
  change job ownership to gain access to jobs that they do not already
  own. SQLAgentUserRole members can view a list of available proxies
  only in the Job Step Properties dialog box of SQL Server Management
  Studio. Only the Jobs node in SQL Server Management Studio Object
  Explorer is visible to members of SQLAgentUserRole.


SQLAgentReaderRole Permissions


  SQLAgentReaderRole includes all the SQLAgentUserRole permissions as
  well as permissions to view the list of available multiserver jobs,
  their properties, and their history. Members of this role can also
  view the list of all available jobs and job schedules and their
  properties, not just those jobs and job schedules that they own.
  SQLAgentReaderRole members cannot change job ownership to gain access
  to jobs that they do not already own. Only the Jobs node in SQL Server
  Management Studio Object Explorer is visible to members of the
  SQLAgentReaderRole.


SQLAgentOperatorRole Permissions


  SQLAgentOperatorRole is the most privileged of the SQL Server Agent
  fixed database roles. It includes all the permissions of
  SQLAgentUserRole and SQLAgentReaderRole. Members of this role can also
  view properties for operators and proxies, and enumerate available
  proxies and alerts on the server.
  
  SQLAgentOperatorRole members have additional permissions on local jobs
  and schedules. They can execute, stop, or start all local jobs, and
  they can delete the job history for any local job on the server. They
  can also enable or disable all local jobs and schedules on the server.
  To enable or disable local jobs or schedules, members of this role
  must use the stored procedures sp_update_job and sp_update_schedule.
  Only the parameters that specify the job or schedule name or
  identifier and the @enabled parameter can be specified by members of
  SQLAgentOperatorRole. If they specify any other parameters, execution
  of these stored procedures fails. SQLAgentOperatorRole members cannot
  change job ownership to gain access to jobs that they do not already
  own.
  
  The Jobs, Alerts, Operators, and Proxies nodes in SQL Server
  Management Studio Object Explorer are visible to members of
  SQLAgentOperatorRole. Only the Error Logs node is not visible to
  members of this role.