Common usage of "strict constructionist" among conservatives is just flatly wrong. So I make it a habit to correct the usage in my posts. Rudy says "strict constructionist" in the same way as most conservatives do, as a euphemism for a constitutional originalist. I saw a discussion and Q&A on CSPAN with Justice Scalia where he describes this distinction in detail. I think it is still on the CSPAN.org website and well worth watching.
He has been clear and unambiguous in saying that he wants to appoint judges in the mold of Roberts and Alito. He wrongly identifies them as "strict constructionists," but that's not so bad as most conservatives wrongly identify them also. They appear (so far) to be originalists, like Scalia and Thomas.
There's no reason to doubt what Rudy means, unless you want an actual strict constructionist, then you are just out of luck.
The term "strict constructionist" is a talking point that Rudy's handlers whispered in his ear in a an attempt to mollify conservatives. Prior to this campaign I doubt the words constructionist or originalist ever passed his lips. His supposed promises on judges is a pig in a poke and I ain't buying.
Conservatives misuse the term all the time. Dubya uses it wrong consistently, most senators on both sides of the aisle use it wrong, and so does Rudy, and so do most of the candidates (I think all of them), and most of their interviewers (have never seen one make the distinction). I have seen Scalia make the distinction, and of course I encountered it in Law School.
I always watch it when Scalia is on CSPAN (usually Saturdays courts hour on CSPAN2), and I know the session you mention. He was very clear that his approach is originalism, and it’s clear from the usage of ‘strict constructionism’ on the part of most conservatives (and almost exclusively on FR) that they mean ‘constitutional orgininalist.’
And another problem I see on FR is the fairly simplistic approach that someone needs to personally be pro life in order to be against the Roe decision. It really doesn’t mean that someone will necessarily vote one way or another on Roe. A pro abortion person or a pro lifer can feel Roe was wrongly decided.
Rudy has been unambiguous that he would appoint judges in the Roberts-Alito mold. Frankly that’s the best pro lifers can hope for now, and it’s good enough for me. And it doesn’t matter much if Roberts or Alito are personally pro life, either.