Well the Gospel writer Luke who has been called one the of the world's great historians (regarding things that can be verified by historical and archaeological evidence) wrote that the apostle James was martyred. That is real historical evidence, ask any historian.
Not only that but this great historian Luke reports the apostles were constantly preaching even though they knew it was extremely dangerous. The book of Acts Chapter 5: 17-42 reports the apostles were thrown in jail for preaching weeks after the resurrection and the very next day they were out preaching again. They were flogged because of that and threatened again with jail but they still kept preaching daily
Acts 5: 40 They called the apostles in and had them flogged. Then they ordered them not to speak in the name of Jesus, and let them go.
Acts 5: 41 The apostles left the Sanhedrin, rejoicing because they had been counted worthy of suffering disgrace for the Name. Day after day, in the temple courts and from house to house, they never stopped teaching and proclaiming the good news that Jesus is the Christ.
So we have historical writings from a known great historian that the apostles were continuing to preach even though they had been put in jail and flogged for it and warned not to do it anymore. Does this sound like an environment where the apostles could be martyred like Stephen (reported by Luke) and the apostle James (reported by Luke) - yes, most definitely. So we have definite historical evidence people at that time were being martyred and we have historical evidence that the apostles were "daily" engaged in activities that could have gotten them at the very least put in jail and flogged; and if fact did get them put in jail and flogged.
Oh, I know, now some skeptic may say but it's in the bible. And I say the NT writers never heard the word "New Testament" or Bible because the Bible didn't exist yet. These men (like the physician Luke) were reporting on the facts and information of the day just like any reporter or historian would. The fact that their writings became part of a book (the Bible) officially formed hundreds of years later does not affect the historicity of those writings (especially regarding Luke).
And then there are the apostles Peter and Paul. We know both of them ended up preaching in Rome of all places.
http://www.internationalskeptics.com/forums/showthread.php?t=85633
Does that sound like a dangerous thing to do under the reign of Nero who was impaling Christians and setting them on fire to provide light for his parties?
Given all of the above, it is certainly reasonable to believe that the oral tradition evidence (which was very important in that day of little literacy and no paper) regarding the martyrdom of the apostles was accurate.