Peter and the Gospel of Mark

The notes at the back of my NIV bible state, "Ancient tradition certifies that Mark was a companion of Peter. The book [gospel of Mark] is called Peter's gospel by some ancient writers. It is generally conceded that Peter may have furnished or suggested much of the material found in the book." (page 1532)

If this is true, I wonder why Mark doesn't name Peter as the disciple striking the ear (Mark 14:47), or why Mark doesn't bother recounting Peter's miraculous catch of fish or reinstatement by Jesus after he was raised from the dead as told in John 21. You'd think this would be one of the most important conversations of Peter's life, yet Mark doesn't mention it! Something doesn't add up.