Aha, I think I understand now. How about this...
SELECT ParcelID from Field_Data where ParcelID not in
(SELECT ParcelID from GIS_Data)
Are any rows returned? Do all of the records in Field_Data have corresponding ParcelIDs in GIS_Data? I bet they do, as you describe GIS_Data as the parent.
In this case, your foreign key is pointing the wrong way, and you really want to create the contstraint on Field_Data to reference GIS_Data.ParcelID. Unfortunately, like you stated... there are duplicates, so a Unique constraint cannot be created on the column, and therefore a Foreign Key can't reference it.
To do so really requires, as you said, normalization... or the use of a different key. Based on your statement that you don't need a strong link, a foriegn key is probably not necessary. Sure, good database design protects integrity, and in this case you are depending upon the application to get it right. Not best practice, but a practice nonetheless!
Todd Carrier
MCITP - Database Administrator (SQL 2008)
MCSE: Data Platform (SQL 2012)