[2h]

> Vatican is entirely encircled in Rome, therefore any area outside Vatican is closer to Rome than the Vatican

this is only true if the rule is "any point inside the area". if the rule is "any point on the border", then your comment fails here:

    +--rome-border
    |
    |
    | x (closer to vatican border)
    |
    +--vatican-border

[Georgelemental]

The official city limits of Rome extend quite far out into the countryside (all the way to Ostia), so by this reckoning, I think the Vatican area would encompass the lion's share of the buildings/population.