Managing Alerts denied on some alerts if permissions are missing

I, as a Site Collection administrator, can create an alert for any user on any library or folder, no matter what the permissions for this user on this lib/ list/ folder actually are.

Now in return this user can theoretically modify or delete this alert, except he can't. If this user has only read permission on a document library or only certain folders in this library, he can view this SPAlert, but he can not modifiy it, to make it a weekly report, instead of a insant report.

I have tried to create a new permission level, calling it "Read and notify" checking the read permission and the permission to create notifications. But this again, doesn't work, if the user can only read the document library.

Is there a way to give a user the possibiliy to add notifications to a list for himself despite missing permissions?