Yep definitely think they are swamped. I received my welcome pack and pins in the mail and then got a text message last Friday stating:
ANZ: Due to unforeseen circumstances, your new ANZ credit cards have been delayed but should be delivered to you by 30/07. We apologise for any inconvenience.
Got the same text myself.
Had already applied for, and received (and spent the requisite $1500) on a standard card about two weeks prior - after reading a few posts in this and other threads on the topic about people doing tens of applications a year, decided my 3rd in 12 months wouldn't be a problem so went for the black as well.