IMHO Iran is just providing a puff piece for their own internal propaganda machine. An American carrier battle group is probably the most powerful war machine on the planet. Apart from the carrier itself, the group has incredible self defence capabilities.
These vessels are armed with a range of weapons, not least of which are vertically launched standard missiles specifically designed to counter air and anti ship missile threats.
Iran is boasting that they have a stealth missile. That I would have to dispute. I suspect what they have is just a sea skimming missile that is difficult to pick up amongst the sea clutter, that plagues sea born ship’s radar.
However the carrier battle group will have an airborne Hawkeye AEW aircraft almost certainly aloft. These have sophisticated look down radars that can sort out targets from the sea clutter. This aircraft can control the battlegroup’s response to any missile or other threat.
Those assets that are controlled will have a very large arsenal of surface to air missiles available to them and will be able to ripple fire these off at the small number of sea skimming missiles that would be available to the Iranians. (You can only carry a small amount due to their size).
Finally. (I bet you’re glad now). The carrier has her own defences namely the RIM-116 Rolling airframe missile, specifically designed for defeating anti ship missiles. And as a last ditch, the Vulcan phalanx CIWS (Close in weapons system).
What do you think. Have I made my case?
PS. I’ve witnessed several phalanx firings. A hit on target every time.