ArcGIS Online allows a user to upload CSVs, but as we found out, this feature provides less extensive sharing capabilities than other comparable cloud hosting services.
The documentation describes CSV hosting. It is possible to upload the file for others in a group to download, but it seems that the ability to share the CSV, a link or as something that could be added to multiple maps, is only available when a premium subscription is activated.
In lieu of a premium subscription, an excellent option is to host the CSV with Google Docs and share the URL with relevant parties. They can then add the CSV to their invididual ArcGIS Online maps, as this blog post shows. The downside with this approach is that it does not integrate with your group as set up on ArcGIS Online. You will also need to publicly share the CSV from Google Docs, since that is the only way you can expose a URL (without some kind of additional programming). Thus, the downside to this approach is for mostly for organizations that have particular data sharing requirements.