Yes, yes, yes!!!
The problem here is that there are some people on one side who will attempt to make it appear as if the President intentionally lied and there are some people on the other side who will deny that there was any mistake at all.
However, when all is said and done, if the White House handles the issue properly, most folks will understand that it is, as you say, "just as simple as it looks on its face."
Well, I certainly hope so, SS. To be honest, I think most people would have had that simple impression if the media wasn't working overtime to make them think otherwise.
I listened to Michael Medved (a brilliant conservative radio talk show host) the other day, and he put this issue in context by playing clips of that entire section of the speech. There was no lie or even inaccurate information (check the wording of the sentence if you doubt me) in the SOTU address, but people have that impression now, thanks to the media.
As we are all aware, journalists can be breathtakingly irresponsible, and unfortunately they have more power than they probably should.