I actually used your question with my brother in the conversation I mentioned in this thread.
If one says “No, Peter did not speak infallibly on Pentecost”, then one must have the conclusion that the Scriptures are faulty. If one says “Yes, but it is because it is Scripture”, then one must conclude that the events of Scripture are in some way ahistorical, really outside regular time and not really connected to us.
So, if one wishes to maintain the reliability of Scripture, with the eternal nature of God, one must say that Peter both spoke infallibly at Pentecost and that it is possible for people to speak infallibly now. The questions then become:1) When and where does this happen? And 2) How can one tell when it happens?
For that, there are three main answers, as far as I have seen. Only one really has the potential to speak as a living voice today in order to settle disputes. The others tend to get bogged down in questions of semantics and reliability.
As an aside: Thank you for recommending those documents. Lumen Gentium was one of the clearest takes on ecclesiology I have read.