You might have a point on the terminology (though you could point out that the way you described the terms is not a standard convention).
But the attack on "intelligent design" gets twisted also. To me, the gaps in the fossil record mean that there is a possibility that we are "lab rats" and there is absolutely nothing in the biological fields of scientific observation to disprove progressive genetic engineering. (It would be an enormous amount of genetic tinkering - over the whole earth!)
We could live on a planet where life is spliced by non-humans. Even the United States government feels it is possible that biological life (whether indigenous to earth, from ancient Mars, from another solar system, or from the (further out) stars) can possibly live underneath the earth & there could be an advanced civilization that existed from as far back as over one billion years ago.
Intelligent design is something that is loudly promoted by theistic evolutionists (vocal progressive creationist joined to the hip, as well), but a far more moderate theory is increasingly seen as remotely plausible - humans probably aren't alone, life could have evolved far earlier than we think (or thought, as island trees were certainly possible over one billion years ago), most islands & continents are completely destroyed (especially pre Cambrian) by plate movements, and UAPs are increasingly seen as something non-human if they can be conclusively demonstrated to NOT BE FOREIGN (HUMAN) GOVERNMENT TECHNOLOGY.
I am amazed the Covid-19 debate, over the lab verses nature, has not clued us in on the mistaken assumption that "intelligent design" musing involves theories only on agencies that are based on divine intervention schemes. (Although the ancient Christian "gnostics" would have a good time with creation schemes and the chain of agents - Colossians 2 comes to mind, read good translations (NRSV?)).
Intelligent design is something that suffers misappropriation, and it is worse than (Dredge aside) the typical references to "atheism" getting misused.