I'm on AT&T and on a corporate BES, and this is what I've found about the BlackBerry Browser.
First, I have three Browsers - BlackBerry Browser, Internet Browser, and MediaNet. They all appear to be the same program, but with different settings (by default), and different routing.
My BlackBerry Browser routes through my company's network. I know this because if I attempt to go to a web page that the company has blocked, I get the same blocked site message that I would get if I were browsing on my computer at the office. This browser is set as the default MDS browser by default (Options --> Advanced Options --> Browser).
My MediaNet Browser routes through the AT&T Network. I know this because if I try to go to www.yahoo.com on it, I get a MediaNet page rather than the standard Yahoo home page I get with either my BlackBerry or Internet browser. This browser's home page is locked to AT&T's home page (http://home) which further proves that it's routing through AT&T's network as this could only be resolved by "local" DNS and is not a legal Internet DNS name. Also, I can't set how the browser starts up as I can with both the BlackBerry and Internet browsers (which can be set to start with either Bookmarks, the home page you set, or the last page loaded). This browser is set by default as the default WAP browser (Options --> Advanced Options --> Browser).
My Internet Browser connects directly to the Internet - I get the real Yahoo home page if I go to www.yahoo.com, and I can access web sites blocked by my company. I have this set as my default Browser (Options --> Advanced Options --> Browser) but it was originally set to MediaNet.
I rarely use either my BlackBerry Browser or my MediaNet Browser, and have my default Browser set to Internet Browser (Options --> Advanced Options --> Browser).
So back to mpenny's original post, try changing your default browser. Perhaps t-Mobile is doing something similar with your WAP browser. Try changing your default browser to Internet Browser.
Also, under Options --> Security Options --> General Options, check the setting for Lock Handheld Upon Holstering. If it's set to Yes, change it to No. You can always lock the device by using [Alt][Enter] at the home screen, and if you have Dial From Home Screen set to No in the Phone Options --> General Options, you can also lock the device with the shortcut key K.