What happens when the determiner is missing?

Phrase 1:

Police officers have the authority to arrest people.

Phrase 2:

All police officers have the authority to arrest people.

As I understand it, the all in phrase 2 is a distributive determiner. How is an absent determiner treated, as in phrase 1?

My subconscious knowledge tells me that an absent determiner means that the statement applies to members of the group generally but leaves the possibility that it may not apply to some. Whereas the all determiner makes the statement explicitly applicable to all members without exceptions.

Is this accurate?