Currently, scripts/ApacheAccessHandler.py doesn't distinguish read and write requests for Mercurial like it does for git and SVN. Thus, it requires WRITE permission for all requests and it is impossible to grant read-only access.
scripts/ApacheAccessHandler.py
Specifically, see the get_permission_name method in that script
get_permission_name
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Specifically, see the
get_permission_namemethod in that script