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The Iowa class battle ships were similar to to battle cruisers in that they were not armored heavily enough to withstand hits from comparably armed battleships. That wasn't a fault of the designers so much as a limitation that the Iowa class had to be small enough to travel through the Panama canal. The Iowa class could fit with just a few inches to spare.

There were plans to build the Montana class of battleships that would be protected with enough armor to take hits from 16" guns, and it would have had 4 turrets with 12 guns total, but it would have been too large to transit the Panama canal. The Montana class was put on hold in May 1942 due to the ship yards where they were to be produced being occupied building Iowa class battleships and Essex class aircraft carriers. The entire Montana class was canceled in July 1942 after the battle of Midway demonstrated that the concept was already obsolete.

From the source you linked.

One supposed distinguishing factor between the classifications of battleship and battlecruiser is that the former can resist the effects of guns similar to those it carries, at least in the "citadel" where armor protection is concentrated, so that a duel between battleships becomes a slugging match. This is known as a balanced design. However, the resistance to shells depends more on the state of the delicate balance between offense and defense which exists at the time a ship is designed than it does on overall design philosophy. The Iowa class battleships had excellent armor protection, but would have been considered under-armored against an opponent with guns equivalent to their own. However, the Iowas were true battleships. They just happened to have what were probably the best (though not the biggest) large naval guns ever deployed. Those guns were very accurate, had very good range and the armor piercing shells they fired were very good at their job.