The Nice and Accurate Prophecies of Agnes Nutter, Witch
Burgomaster's privilege is modified in 2010 FAQ.
Note that the FAQ for Lupusburg (English, Italian) which is dated 2010 (thus more recent than the above clarification), has a modification to the Burgomaster privilege:
Lupusburg FAQ wrote:
Q02. Can you explain the privilege of the Burgomaster in detail?
A02. The privilege of the Burgomaster is modified as follows. He chooses one living character: the owner of that character secretly shows it to the Burgomaster, who must then secretly show one of his own characters to that player.
The use of this privilege is not mandatory.
If I read the above correctly, the Burgomaster option #1 to see another player's living character for "free" (i.e. that the Burgomaster doesn't reveal a card) is gone. All use of the privilege is as the rulebook's option #2: an exchange of information about living characters (of the Burgomaster's choice in both cases), but there is no longer a restriction against the sole living character of players. As before, use of the privilege is optional.
As someone who's only played Lupusburg a couple of times, but neither time played it correctly due to similar confusion over how option #1 applies, this helps make the rule simpler and (apparently) fairer.