I think that is because they are using https://dev.twitter.com/docs/api/1.1/get/statuses/sample

This is dev stream and it has tiny number of tweets.

Yes I think that was mentioned in the copy. It's also not really "random." It's one of the last 20 tweets globally. You probably won't ever see a tweet older than a few minutes.

It's actually because Twitter rate limits the oembed endpoint by IP, so the app caches the oembed codes and uses those if it gets limited. I've been meaning to flip that bit to the client but haven't gotten around to it yet.