NP-Complete Problem and Polynomial Hierarchy
$\mathrm{SAT}$ and all $\mathrm{NP}$-complete problems are certainly in $\Sigma_2^P$, as $\mathrm{NP} \subseteq \Sigma_2^p$. It is true however that if $\mathrm{SAT}$ (or any $\mathrm{NP}$-complete problem) ever gets proven to be $\Sigma_2^p$-hard, then $\mathrm{NP} = \Sigma_2^p$, and consequently the polynomial hierarchy collapses to $\mathrm{NP}$.