Hi Kristi,
what makes you think that the servers are owned by "Everyone's Internet, Inc"?
Most of our servers are operated by one of the world's biggest server-hosting company and are physically located in Houston, TX.
Of course, the reason that avast is periodically trying to contact these servers is the auto-update feature. If you're not comfortable with this, you can disable the auto-updater by accessing the Settings item in the menu in main avast application.
Hope this helps,
Vlk