Or most murder investigations are (by definition) incompetent.
Or (more likely): The old idiom quoted above is stupid and useless. (That it presumes that murdering and getting away with it is somehow a noble or esteemed deed should be damning enough.)
There’s no money or benefits in solving crimes. It could be done easily in many cases but nobody cares about certain people like gang members. Lots of cases where the murderer tells everyone but nobody cares.
Which part is wrong? Only 2/3 of these to choices can be wrong. The remaining one must be correct.
In both cases, the premise is unclear so good luck!
The 4th option they may appear to propose suggests that murder investigators don't get paid -- neither in money, nor in benefits.
So, to that end: As far as I know, that's not usually the case with government employees, and it is always actionable when it does happen to be the case.