Merging with Battle.net password verification

I'm attempting to merge my World of Warcraft account with Battle.net, but its now asking World of Warcraft® Account Verification

Enter the username and password of the World of Warcraft® account you wish to permanently merge into this Battle.net account. You will have the opportunity to merge additional accounts after this process is complete. After merging, you will use your Battle.net account e-mail address and password to log in to this World of Warcraft account.

I'm probably just being overly cautious but I've been told repeatedly that Blizzard will NEVER ask for your password.

So my question is, Is it safe?. (a Blue response with a simple yes or no would suffice)