The difference being that the commendations a generalized to weapon classes, so there are many of each class to choose from placed on the map. Precision works because the DMR and NR are grouped in with the sniper. Specify which and you will have betrayals, no question, because you're actively rewarding them to do so (your example was that there would be an achievement or substantial reward for this behavior, not sure why you're claiming otherwise). Sidearm is a bad example, because you spawn with one, its not a map pickup, which would be a problem otherwise because it is specific and thus limited. Look at specific daily challenges: on sticky days, that's all people do and they'll vote hard for Elite Slayer, assist days they stop firing after four shots. You might not see it happen, but you have to assume as a designer that there are terrible, awful people playing your game. It happens.
And yes, I've seen people get angry because they were trying to pad their Rear Admiral and Wheelman. Anecdotal evidence is anecdotal.
Edit: with your post above, I don't see how that's any different than current Commendations other than increased rewards for milestones, which still becomes tricky in non-MP settings (in the case of the MP Inheritor rushes early this year, it's applicable to multiplayer as well).