Can a commander give a letter of reprimand for being a passenger in a car?

Yes happened at Fort Drum with the reasoning you shouldn't let a battle buddy drive drunk nor get in a vehicle with someone you know is intoxicated

They probably expect soldiers not to get in the car of someone that is drunk. If the passenger is sober, he could drive.

I never have heard that one but talking while intoxicated (Insubordination) - Yes.

Short answer: Yes.
Longer answer: The Commander is responsible for enforcing good judgement for all members of the Unit, regardless of what role the unit member is playing. If you are a passenger of a car that is being driven by somebody who's UI then you needed to say something, do something, use good judgement.

They are lucky it's only a locally filed letter. I've been in commands where the passenger gets an Article 15. For people stationed in Japan, everyone in the vehicle gets a DUI even if they're asleep in the back of the car.

Passenger sober and knew driver was drunk? Oh yea, LOR coming. Passenger drank and knowingly got into a car with an intoxicated driver? Yep, LOR coming.

This is just my opinion but if you are in a car with a guy who you know is drunk and you are not you shouldn't have let him drive. If he wouldn't listen I wouldn't have stayed in the car. I never had an issue with a guy who was wasted letting me drive them back in their car because I didn't drink. As far as the letter, I can't give you an answer on that one. Never saw that happen.

A reprimand could be seen as getting off easy. There are states where you can be charged for allowing an intoxicated person to operate a vehicle.

I love how everyone is assuming the passenger knew the driver was intoxicated. I can think of a few instances where the passenger might not have a clue about the drivers sobriety. My old supply Sgt and I drove across country for his pcs. He was tired and stayed in the car and slept while I went into the grand ol opry for an hour and a half. I could have had several drinks while I was inside and he would have never known.

Yes, a Service Member could be reprimanded for being a passenger in a car driven by a person under the influence. This shows very poor judgement on the part of the passenger. If the passenger was sober, he/she should have insisted on driving. Drunk or sober the SM should not have gotten into the car with a drunken driver. At best the passenger failed to care for their fellow SM when they were intoxicated and put both of their lives in danger.

I'm assuming this involves two or more junior enlisted members. The driver is in deep trouble. The passenger is lucky to get away with their life and a letter of reprimand. Both SMs demonstrated very poor judgement and behaviors unbecoming a member of the Armed Forces. Young people make stupid mistakes. Hopefully they all learn from this experience.