Campo Santo Teutonico

I was told that the "Campo Santo Teutonico" (Teutonic College and Graveyard) within Vatican City (number 60 on this map) is actually technically not part of Vatican City, but the last little bit of the Holy Roman Empire. Supposedly it is administered jointly by the ambassadors of Austria, Germany, Belgium, and Netherlands. (The only confirmation of this I've found on the web is in German, and says that this was part of the 1929 Lateran Treaty that established Vatican City.
Also: the border on this map shows it not being part of VC.)

(Click below for interior view.)