ArcGIS Online customers are moving their companies to Enterprise Organizational Accounts. The documentation for Configuring the Map Viewer discusses how to define the default basemap. The share settings required for the group and the maps are not mentioned. Customers need to be aware that a group can be public or open to the organization but when the basemap is private, the map is not available in the drop-down menu. Customers also need to know that making a map public or open to the organization, but having the group private, makes the group unavailable in the Basemap Gallery.
This can be an issue if there are basemaps that individuals want to use for their group. For example, the basemap for the sales team may want the sales territories in their basemap. The delivery team may want to have a basemap with driving routes. These basemaps would only be available to their groups and not to the organization as a whole. The organizational account manager must choose a generic basemap that is available to the entire organization and that may not suit either group.