The reason is because lowering the entropy of the password makes the blizzard version easier to crack. If blizzard is compromised, the passwords won't be disclosed - just the hashes will be, so re-use isn't immediately an issue. It becomes an issue when the hash is cracked and the attacker can now see which password is being reused, and then reuse it. Of course if the reused password is something like "hunter2", the cracked version will look like "HUNTER2", but the original case can be guessed in a few tries once the case-insensitive version is discovered.
Very roughly, case sensitivity provides about a half bit of entropy. For reference, one bit of entropy takes twice as long to crack.
And say what you want about password reuse, but 99% of users re-use passwords at least somewhat, so site owners have an obligation to protect user passwords.
And the random salt used for hashes, and the minimum length of 8 for your password, all but eliminates their database compromise as being a plausible vector of attack.
Plus, caps doesn't add that many bits of entropy, when used as people use it (first letter, alternating letters, etc).
Very roughly, case sensitivity provides about a half bit of entropy. For reference, one bit of entropy takes twice as long to crack.
And say what you want about password reuse, but 99% of users re-use passwords at least somewhat, so site owners have an obligation to protect user passwords.