Using a newly created site, I am unable to access the REST API using the example provided:
curl -u {username}[:{password}] https://{account}.VisualStudio.com/DefaultCollection/_apis/projects?api-version=2.0
returns<html><head><title>Object moved</title></head><body><h2>Object moved to <a href="....">here</a>.</h2></body></html>