At least, I think it is referring to the Physical Table, but changing the name of the Physical Table doesn't change the error message, though changing the Logical Table name does, so I'm not really sure what it is referring to. Here is what one looks like precisely:
WARNINGS: Business Model [Business Model]:  Logical dimension table [Logical Table] has a source [Physical Table?] that does not join to any fact source.
Now, each of the three multi-level dimensions have a base level with a key that is present in the Fact Table. I can even right-click on the Fact Table on the Business Layer and go to Business Model Diagram or Physical Model Diagram and get a diagram of my fact table linked to all of its dimensions, including the three in question. Analysis made in OBIEE work so long as I don't use those three dimensions.
 Logical dimension table Time has a source TIME that does not join to any fact source.