To the best of my knowledge, this is not true. If your BB finds a WiFi network that you are able to connect to then it can use that for surfing. However, there are some apps that while they appear to be using WiFi, there is some data being sent over the BIS/BES server and you will be charged for that. One that comes to mind is iSkoot, an application that allows you to connect to your Skype account.
Panny TC-P60GT50, Vizio SB3651-E6 Soundbar, Harmony One, Android Box