you should be able to see all Person ID in your workbook if query is bringing them.
create calculated field for Person ID and drag that on your worksheet to see if you are getting all of them
IF ISNULL(Person ID 1) THEN [Person ID 2] ELSE [Person ID 1] END
Also please make sure you do not have any data source filter which is filtering out data from one of the tables.
I tried joining on two other fields and it worked fine as long as I didn't use that field that wasn't fully present in both datasources. This is not how I would expect Tableau to work but alas it seems to be working so far....