I often encounter a URL containing pbs.twimg (example: https://pbs.twimg.com/. Is this a legitimate PBS URL?

No. PBS does not own, manage, or control those images and is in no way associated with images at that domain. The pbs.twimg.com subdomain is Twitter's image-hosting domain and PBS stands for “Photo Blobstore.” More information can be found at https://blog.twitter.com/engineering/en_us/a/2012/blobstore-twitter-s-in-house-photo-storage-system.html.