I am certainly not thinking that. I think Dr Paul explained this reasonably carefully: he was pointing out that just because it is a common carni food it does not mean it is not inflammatory.
And there is always the question of the extent of the inflammation, which as far as I remember was not discussed. As you said, some inflammation in the body is normal in response to every day stressors. If eating eggs is inflammatory, but only a bit, then I reckon it’s worth eating them.
But if someone like Robin (a robust carni eater!) gets a whacky CRP score, then I reckon it’s useful to understand this.