You are correct that ideally the mezuzah should be placed outside the door so that one encounters it upon entrance and also to ensure that the whole dwelling is protected. Your desire to proudly display your mezuzah is also commendable.
However, since, in your case, the mezuzah would thus not be within the doorframe and under its lintel, it is questionable whether its placement would fulfill the Torah’s command. Your neighbors have done correctly, as the entire doorframe — even the part behind the door — is acceptable for mezuzah placement. This is true even if the mezuzah is obscured by the door when it is open.[A]
When there is absolutely no room on the inside of the doorway for the mezuzah, it may be placed on the outer frame without a berachah. [B]
Alternatively, if you owned the apartment, you could dig out a shallow indentation in the doorframe and place the mezuzah there.[C]
[See also question “No Space at All on Post.”]
 Agur B’ohalecha 14:2.
 Mezuzot Beitecha 289:8; Chovas HaDar 8:2.
 Mezuzot Beitecha 289:8. No berachah is recited when one is forced to place the mezuzah on the outer frame, not under the lintel.
 Less than eight cm. deep. (?)