> Why would a thief post a photo of a stolen vehicle?

Casual small time occassional car thieves might do this, receivers of stolen cars as payment for other debts owed by a thief may do this ... but it's somewhat atypical.

> Aren't most stolen vehicles disassembled (chop shops, etc)?

In the organised bigger scale operations vehicles are dealt with for the greatest profit with least risk. A good many are stripped for the parts - the more popular the car, the larger the parts after market.

A suprising number of cars from developed countries are shunted whole into containers and sold elsewhere about the globe. eg:-

  “Each year, hundreds of thousands of vehicles are stolen around the world, yet the initial theft is often only the beginning of a vehicle’s journey into the global criminal underworld.

  “Stolen vehicles are trafficked across the globe, traded for drugs and other illicit commodities, enriching organized crime groups and even terrorists. 

Going back to the the article, you have to find a picture of your exact car online somewhere, then use GeoSpy to tell you it was stolen in the US and was photographed in Columbia, then you go to that place in Columbia to find it's not parked there anymore, so you contact the person who made the post/listing and try to arrange a meeting, then you confirm it's your vehicle, then... what exactly?

Local police are doing none of this btw.