"but [B].[UNIQUEID] and [B].[FIELD001] are themselves being pulled from a different source."
How is this data being "pulled"?
If these are calculation fields, you have an unstored, unindexed field it cannot be used on the "many" side of a relationship like you have here. This has nothing to do with whether the table is internal or external.
I actually have no idea how any information is being imported into DB B as I didn't create it and (I believe) it's locked to everyone except the creator... also, I have no idea who that is.
The fields aren't calculations, just text fields.
I also thought that there might be an issue with the number of records in DB B, but there are only about 200K.
I think it's something weird going on with the database. I just recreated the the same relationship in a new database and it worked perfectly fine.
Since you can enter a log in and password to connect to the file, I would think you could open this file directly with that same log in and password to check its design.
Check to make sure that the data types for the two ID fields are both text and that they contain exactly the same values when they are supposed to match. (even a trailing space in the ID field of one table that's not in the ID field of the matching record in the other field will keep them from matching like they should.)