Most people who keep talking about these protections, all the way up to the president, continually characterize these protections are so broad that it's almost impossible to sue a gun manufacturer while also acknowledging that Remington settled a lawsuit for $73 million (more on that later). This is why it has to be a lie - you're telling people that they can't be sued while being aware that they can be.
The protections don't extend to companies being sued for damages for which they are directly responsible. If they checked the gun that Alec Baldwin was using on Rust and found a factory defect that caused the gun to go off when it should have, it would be very easy to sue them. The point of these protections is to cut down on frivolous suits. Nobody was calling for lawsuits against car manufacturers after that maniac plowed his car through a crowd of people. Likewise, if that happened because the brakes were improperly manufactured, the car company could, should, and would be sued.
The problem for the people pushing this lie is that the Remington settlement is an argument for those protections. The lawsuit was entirely without foundation; but, all you need is an activist judge and an unscrupulous lawyer to get the suit passed into the court process.
Remington broke no law and breached no contract. The gun functioned the way it was supposed to. The lawsuit attacked some of Remington's advertising, which I'll admit was ill-advised; but, there's no evidence that the shooter saw the ads and we know that he didn't buy the gun.
Still, civil law is often abused. No matter how valuable it is, the cost and the risk is generally low for the plaintiff with the potential rewards being high while the risks and costs to the defendant are always remarkably high. Even with these protections, Remington felt compelled to fork over $73 million even though they did nothing wrong.