If the bill doesn’t specify the “original” birth certificate, its actually providing cover for Obama.
But, yes. We already know that while he may be “native born” he is self-admittedly not “natural born” as his father was not a US citizen (presuming the father of record to be Obama senior).
And to be a bit clearer, I’ve always said that it isn’t just the birth certificate in question, its the follow-on question of what citizenship did he claim in college and what passport did he travel on when he went to Pakistan. Those are three bits of information he has kept sealed away, and you have to assume he has sealed them away for a reason.
As far as I know, there is still some question as to whether or not he obtained scholarship funds to Columbia for which only foreign students were eligible. If that's true, and if he was an American citizen at the time, that's fraud, and based on tuition costs at Columbia, probably a felony, although the statute of limitations has probably long since expired.