Google also indexes this data. Craigslist obviously doesn't own this data as they have DMCA practices in place. They can't claim DMCA and also say that the data is their data.
That is a power that, in the past, Craigslist has used for good. In this case, it's a power being used just for the benefit of Craigslist to protect its network effect incumbency, to the detriment of users.