Is it legal to use windows 7 home premium as business?

No it isn't illegal, Home Premium is for the home user and focused around Entertainment, And business is for business and focuses on Security, Reliability, Remote Desktop, Etc.

If it's just a normal Home Premium licence, you can just use it at business as you please.

The name is for branding purposes (and to indicate the features enabled/disabled on it). It has nothing to do with its licensed use.

For instance: As per the MCITP 70-680, the only difference between 7 ultimate and 7 enterprise is volume licensing (available in enterprise, not in ultimate)

Not illegal, but for larger businesses (ie have a server and more than a handful of users) the benefits of using Active Directory become greater, and the Home editions simply can't be added to a domain, so for those situations it's a matter of practicality not legality.