I had the same problem and I think that it is a bug in SSIS.

When you select the table to be populated in the drop down list in the OLE Destination component, you have the "Name of the table or the view:", you get the owner of the table and the table name i.e. dbo.table1.

Manually go to the dtsx package and search for the entry dbo.table1 and add the database name to it as well, i.e

MyDB.dbo.Table1

When you go to the OLE Destination again, it will show the database, owner & table. This should sort out our problem.

PS, you will not be able to select the table again from the drop down box as it will only populate it again with the owner & table name which will fail again.