Go to your Blackberry menu, and then Setup. Choose Email settings, then highlight the one you want to edit the signature for (I have different signatures for different email accounts). When it is highlighted, hit the BB menu key, and choose Edit. Scroll down till you see the signature field, delete the text and create your own, or leave it empty. Scroll to the Save button and save your changes.
Try this Method, works for me.
I tried reading through that thread and it was confusing. ALthough the correct answer (IMHO) was there, several replies also referenced logging in to your BIS account via the web browser and that's not necessary at all; you change the signature for your email accounts on the device itself through the email setup. Unless I'm missing something? (This is entirely possible, since I am very new to Blackberry. Educate me!)
Just after you posted this question, there was an interesting article posted over at Crackberry.com. Check it out at http://crackberry.com/quick-tip-how-modify-e-mail-signature-your-blackberry-device-0