Stack Exchange team used to create a Twitter bot for every site (except Stack Overflow, due to its volume of posts). The Bitcoin bot is one of those. You can see all SE-created bots linked on the list of sites.

However, these bots turned out to be not very effective tools for promotion, and Twitter had some objections about this large number of automatic accounts. So, SE team decided to stop creating Twitter bots for new sites; the sites launched in March 2014 or later do not have them (with exception of localized SO sites, which are special projects).

The Ethereum site, being recent, does not have an "official" Twitter account, so a community member made @StackEthereum (and then another user made one more, being unaware of @StackEthereum). Monero could have one too - making a Twitter bot is not too hard.

One doesn't need anyone's permission to post links to site's content on Twitter. The main thing is to make sure the bot doesn't annoy Twitter users; if those following a low-volume hashtag find it flooded by robotic tweets, they will be displeased and that will reflect poorly on the site.