Users do not have permissions to mark issues as "fixed" even if they reported the issue.
I found out that a bug I was having got fixed in a recent round of updates:
I selected status: 'close' since 'fixed' was not available, and I thought it was a close approximation. Selecting that option hid the issue from the issue tracker and the list of 'my issues'.
If you don't want people to mark their own issues as resolved, maybe it doesn't make sense for the 'closed' option to be there either.