It absolutely does in this regard. 100%. Trust me.
Lawrence is not a public schoolboy. The original comment was a little tongue-in-cheek. But no-one has spoken of shielding him in the way they have spoken of shielding Pope.
Ever heard of Hitchens’ Razor? “That which can be asserted without evidence, can be dismissed without evidence”.
“Trust me” holds about as much water as a colander. Our two most shielded players (Stokes and Root) attended academy status schools - not fee paying.
Lawrence has been shielded, he went on several lions tours before converting to the first team, and then batted in his usual position rather than be shoe-horned in (ironically like Pope was when made to bat 3).
As Others have said, you’ve not presented a shred of evidence that the batting order is “based on class”, so as such this claim can be dismissed out of hand 🤷♂️