Search Filter for Activity Type in Case Mgt screen does not display activities where component is Contacts AND Case

Activity Types created where Component is Contacts AND Cases do not show up in the Search Filter for Activity Type in the Activities section of the Case Management Screen for a case. It does show up in the Add Activity listing.

From Administer/Customize data and screens/activity types - Create an activity type where the Component is Contacts AND Cases.
Edit an existing Case Type and add this activity to the case type.
Create a case or use an existing case of this type and in the Manage Case screen, use Add activity to add the activity type where the component is Contacts AND Cases.
In the Activity section of the Manage Case screen use the Search Filter for Activity Type.
The activity type you created where component is Contacts AND Cases will not be listed so you cannot filter on this activity type.

This is the same on the CiviCRM 4.5.4 sandbox and a client's 4.5 sandbox. Discovered because client cannot yet upgrade but need to start recording activities on Client's live site which will later be Filed on Case. Cannot add an activity whose Component is Case Only to a contact record so needed to configure component as Contacts and Cases