I think you are saying is what the House “thought” and their “judgement” - supersedes NYS election law regarding who is certified as winner?
Article I of the Constitution provides that each House is the sole judge of the qualifications, elections and returns of its members. The House can seat whomever the House rules won the election, even if the state has certified someone elese as the winner—that was quite common in the 19th century, and it happened in 1985 when the Democrat-controlled House pretty much stole a seat when it seated Democrat incumbent Frank McCloskey despite the Setate of Indiana having certified his Republican opponent as the winner (the House had its own “recount” and ruled, on a party-line vote, that McCloskey won the election by 4 votes).