Administator rights allow you to change ownership and delete other people's filters, but I suspect you're looking in the wrong place (because I keep doing it too).
It's in the admin section, not "manage filters". See https://confluence.atlassian.com/display/JIRA/Managing+Shared+Filters
I believe you may be missing some Global permissions like 'Create Shared Objects' for example.
If the Global permissions are set as the default, most likely your user is only a member of the jira-administrators group, but not jira-users and jira-developers.
Hope this helps.
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