Joseph,
Thanks for the extra info. The default basemap is set in the organization settings.
Sign in to the AGOL organization as an admin, and click on "My Organization". Above the list of users you will see a button to "Edit Settings". See image:
[ATTACH=CONFIG]33664[/ATTACH]
You will then see some vertical tabs- click on "Map" and you should see the "Basemap Gallery" and "Default Basemap" sections listed on the right hand side. The default basemap can be selected from the specified basemap gallery group. See image:
[ATTACH=CONFIG]33665[/ATTACH]
I can't access the map you specified in 1, as it's not shared publicly. However, I did manage to create a map successfully with a basemap using the service you specified in 2.
Regards,
Nick