Evangelicals/fundamentalists who believe in biblical inerrancy hold that the Bible is the inspired word of God, and contains no errors.1 This is typically understood to refer to the original autographs of texts that were written by or under one of the recognized apostles (twelve plus Paul).
There are a number of places in the Gospels where the words of the apostles are obviously wrong, such as when Jesus rebukes Peter in Matthew 16:22–23. This isn't a problem to the inerrantist, because the record is inerrant, not the content of Peter's speech.
Does anything change when we turn to the Book of Acts? That is, do those who believe the Evangelical/Fundamentalist view of biblical inerrancy also believe that the speeches made by the apostles are inerrant?
For example, an inerrantist would say that the Book of Acts is inerrant. Thus, Acts 20 is an inerrant record of a historical event (which happens to include a speech by Paul). But, does the inerrantist extend this and hold that Jesus definitely, without a doubt, said the things that Paul attributes to him in that speech?
Acts 20:35 (ESV)
“Remember the words of the Lord Jesus, how he himself said, ‘It is more blessed to give than to receive.’”
Or is it theoretically possible, according to the biblical inerrantist, that Paul was mistaken, or even lying, about what Jesus said?
I'm not specifically asking about this passage, but more generally about all the recorded speeches of apostles in the book of Acts.
A great answer would cite inerrantist scholars who deal with this question. If there is disagreement among evangelicals, I'd like an overview of the positions.
1. For the purposes of this question, I'm referring to those who would sign the Chicago Statement on Biblical Inerrancy.