I solved this myself. I found that, after upgrading to Mac OS Lion from Snow Leopard, some of the aliased folders in my Time Machine backup hard drive are not locked, but the regular folders are locked. Apparently this is new in Lion. (As I mentioned above, my MacBook is too old to upgrade to Mountain Lion.) I had based my query above on my ability to delete things from some aliased folders on my backup hard drive. Fortunately, they are locked in the equivalent non-aliased folders.