Although rare, yes, this does happen with a select few encounters in the game. It is in accordance with the Pokédex entries of the Pokémon in their natural habitats and their choices of prey. Sableye eat gemstones, so Carbink are natural prey.
The only other example in the game is Mareanie (or however you spell its name). It eats coral, and as a result Corsola are natural prey. If you enter into an SOS chain with Corsola, it may call a Mareanie instead.
Source: sumwun and an answer he posted two years ago on a similar, but different, question.