It is a definite "no". It's sad that many of the call center, customer service agents really don't know that much about the rules or even much about cruising. Some will take the time to look it up for you and others will just spout something off the top of their head that may or may not be correct.
Downy Wrinkle Release is a good product and you can bring that. A travel steamer can also be used. The best thing is to pack your clothes in plastic, dry cleaner bags, and pack them in layers in your suitcase with dry cleaner plastic or tissue paper between the layers. If you and/or your wife are good at folding then your stuff will have few wrinkles.
Have a great cruise and leave the iron at home. If you do have a couple of wrinkles no one will care and if they do they are the ones with the problem and not you.