(More a comment than an answer):

I've looked at the [German Wikipedia entry][1] wrt. the emergency numbers:

It's enlightening that `112` is *both* the European emergency number (since 1991) and in Germany historically (since 1973). It is also the emergency number for the fire brigade and the ambulance.

The police historically has used `110` (as explained in other answers).

I would assume therefore that, in Germany, `112` gets a lot more fire+medical traffic than the police one and is a possible explanation for the seeming incompetence of the operator - many locals would call `112` only for the fire and ambulance, and it's indistinguishable whether you intended the (historic) `112` or the international `112` :-)

Quite some other European countries have completely disjoint police/fire/medical [emergency numbers][2] vs. the international `112`.   

  [1]: https://de.wikipedia.org/wiki/Notruf#Notruf_112
  [2]: https://de.wikipedia.org/wiki/Notruf#Die_Notrufnummern