I wonder if the terminology isn't being confused here a bit.
I think that Inerrancy applies to Scripture, but that Infallibility has a much stricter definition than that. It is so strict, that I don't think it could apply to Flat Earth, Creation vs Evolution, The Age of The Earth or The Existence of The Walls of Jericho. The teaching that The Scripture is Inerrant, could accurately be said to be an Infallible teaching, but to then say that, for example, Noah survived The Flood in a boat made of wood, would not be an Infallible teaching, even though it is obviously what The Church, The Popes and The Fathers have always taught and will always teach.
It's like the difference between Graduating from school, getting your Diploma and your Official Transcripts. Your Graduation is evident and can even be documented, but The Diploma gives the fact of your Graduation a greater veracity, than without one. It's like proof. It makes the reality of your achievement much harder to dispute, than it would be without one, because it is an official document, given to you by a body charged with that task. Without that, you may only have your report cards and class schedules to prove the work you had done. But even then, another College will not consider your graduation a fact, without your Official Transcripts, sent to them directly from your former College. Furthermore, the College would be unwilling to send Official Transcripts of your record of perfect attendance, for example. They would not do it, even if they could verify it. You could argue that Perfect Attendance was a requirement of Graduation. So, the implication would be that you had Perfect Attendance, but you would still lack Official Transcripts attesting to that fact and, more than likely, nothing could change that.
I looked over this article, to help with this post: http://www.newadvent.org/cathen/07790a.htm#V