If you want to avoid accidental Internet usage, set up a "No Internet" browser account.
(Note: Below info applies to AT&T phones. Rogers, Fido and other carriers will have slightly different names and possibly menu structure)
Top Menu>Settings>More>Connection>Access Points>New Profile
Enter a Title (ex. "No Internet") and APN (ex. "null")
Save it.
Go back.
Internet Profiles>New Profile
Enter a Profile Name (ex. "No Internet") and set it to use the "No Internet" Access Point.
Go back.
Go back again (you should be in Top Menu>Settings>More)
Applications>Browser>Accounts>New Account
Enter an Account Name (ex. "No Internet"), Home Page (ex. "
http://null"), and set it to use the "No Internet" Internet Profile.
Activate the account.
Now...
Access to the built-in browser (MEdia Net) should fail with "Connection failed!"
Access to MEdia Mall should fail with "Connection Error Unable to connect to server. Retry?"
Access to CV should fail with "Connection failed!"
This won't necessarily block
all Internet access, but it should at least limit the access to the initial name resolution attempt, if that even gets counted at all.
To get back to having Internet access, go to the Browser settings and activate the MEdia Net account.