I didn't say it solves every SAT problem in polynomial time, I said it can

> find satisfying assignments to satisfiable SAT instances in polynomial time

The distinction between this and solving SAT, and the slight strengthenings one can make to universal search, are part of those few technicalities I promised to gloss over.

Also, cut the snark. I'm not a complexity theorist, but my PhD thesis was in the intersection of graph algorithms and complexity (the first word of the title literally being "Hardness"), and I'm more than qualified enough to understand and present well-known complexity results from half a century ago, even when a misguided appeal to authority is at play.