Except in these cases, the passive voice is the only reason it's possible to remove the police officer and still have a grammatically complete sentence (absolute-minimum requirements: noun plus verb). Going back to Highway's original two examples -- "A bystander was struck and knocked to the ground by a police officer" (passive) vs. "A police officer struck a bystander, knocking him to the ground" (active) -- what are you left with if you remove the police-officer clause from each?
"A bystander was struck and knocked to the ground" -- yes, that is a complete sentence. Since it's passive voice, the verbs or verb phrases "struck" and "knocked to the ground" don't require a noun: it's grammatically sufficient to know these things happened, without knowing who or what did them. The be-verb "was" is the key verb in that sentence, and "bystander" is the noun it goes with.
"Struck a bystander, knocking him to the ground" -- no, that's not a complete sentence and doesn't even make sense as a fragment: in the active voice, you need a noun to go with the verbs, because it's not enough that "these things happened"; active voice requires identifying who or what did those things or committed those actions.
Like the cliched politician semi-admitting wrongdoing: "Mistakes were made" (no mention by whom) rather than "I made a mistake."