Morag,
Excellent. You are most welcome and thank you for also explaining the nature of the issue you had, as that will help others avoid that.
The moodle/course:viewparticipants is the capability that is checked for access to the course Participant list.
On the other hand, the SITE capability, moodle/site:viewparticipants, is used at the site level to see the list of all users in various site level tools. It is set to Allow for the Manager role, so the Manager can see everybody and view all user profiles.
(You would not usually want to allow that for all other roles, but it could be useful if you were making a custom role like a site wide auditor role, for instance.)
Also, reminder that there is a useful tool for troubleshooting such issues, the Capability overview tool in Site admin > Users > Permissions > Capability overview. It will show you for any capability exactly which permissions are set for which roles in which contexts including category and course level overrides. Very handy when things get complex ;)
Randy