Are you suggesting that Tacitus and Josephus would have hunted out domestic servants and slaves (who made up the bulk of the church in the first 100 years or so of Christianity) to ask them about the founder of their faith.
First of all why not? Both of them where fairly good historians.
If you call propagandists 'good' historians. Most of their respective works is made up of the reporting of strategic events such as political situations, imperial and military events - ie not the everyday, life on the street things. Yes, not all the Christians in Rome were slaves and servants though Paul's letter to the Romans tends to imply this kind of person. The richer folk were the likes of Prisca and Aquila, who were tentmakers/traders, and generally non-Roman.
Second of all, "the bulk" is not everybody, It should be clear, even to you, that some Christians were well educated.
Actually, people can lead a group, run a business and do a whole host of complex things without being 'well-educated', jeremy. Educated, perhaps. Jewish children - male and female - were usually educated in basic life skills to the equivalent of our middle-school level. It was only the nhigh-flyers who went on to higher, generally theological and other areas of education.
Suggest away. How about some solid evidence for one of your suggestions?
Well, as I have already pointed out, much of their material relates to military, political and other issues. That suggests that their contacts and sources were from the higher eschelons of society.