This is a hypothesis, not a fact. A bad one at that.
It's a perfectly reasonable hypothesis, though. It seems very unlikely that Tacitus, Suetonius, or Pliny had any access to non-Christian or non-Jewish sources about Jesus. They all mention Jesus only in the context of talking about Christians. They know who the Christians are (roughly) and they know that they are followers of Christ (more or less); obviously they know the latter because they know the former. They demonstrate no knowledge of Jesus beyond that. Tacitus seems to think that "Christ" was Jesus' name, and Suetonius doesn't even get that right, calling him "Chrestus" and apparently thinking that he was a contemporary leader of the Christians.
The only one of the people you mention who I think could plausibly have access to knowledge of Jesus that
doesn't come from Christianity is Josephus, since he mentions Jesus in the course of discussing various itinerant charismatic figures of the time, rather than in the course of discussing Christianity (as the pagan writers mentioned do). But there are notorious problems with Josephus' discussion of Jesus. There is little doubt that he did discuss Jesus, but precisely what he said about him is uncertain.
Scholars don't see many contradictions between Christians sources and secular sources that refer to Christ, and since they presume Christianity is not supernatural, they draw the lines that say that therefore the secular sources used Christian sources.
No, that is not a fair reconstruction of the reasoning. It's got nothing to do with whether Christianity is supernatural or not (whatever, precisely, that means). The question is where the non-Christian writers got their knowledge about Jesus from. Why would the supernatural nature or otherwise of Christianity itself have any bearing on that? Would someone who thinks that Christianity is supernatural therefore suppose that Tacitus and Suetonius were divinely inspired when they wrote about Jesus? Why would anyone think that? The question of the inspiration of Christianity may be relevant when discussing Christian sources such as the Gospels but I cannot see how it is relevant when discussing pagan ones. Now the reason why it is reasonable to think that the pagan authors derived their knowledge of Jesus from Christian sources is not merely the lack of contradiction between these two groups of sources (and, as I indicated, there are contradictions between them, at least in the case of Suetonius) but the sheer paucity of information in the pagan sources. They tell us nothing beyond the sheer existence of Jesus and the fact that Christians were his followers. Since the pagan authors could obviously have gleaned that from the barest knowledge of Christianity itself, why posit any other sources for them?
There is no evidence that Josephus', Tacitus', Suetonius', or Pliny's references to Jesus were drawn from any specific writings.
No, but when I say "Christian sources" I don't necessarily mean Christian writings. I just mean that their knowledge came via Christianity rather than via some wholly non-Christian route. For example, Pliny might have heard the name "Jesus" when interrogating Christians - there's no reason to suppose that he read any Christian texts. It seems very reasonable to suppose that all of these people knew about Christianity as a new religious movement, simply because they knew what was going on in Rome and elsewhere, and they knew that Christians were some kind of sect who were followers of somebody called Christ. They might, or they might not, know the additional fact that this Christ was someone who was executed under Pontius Pilate. And they wouldn't have to have any access to non-Christian sources to know these things - they would know them because the Christians themselves made no secret of it. Why hypothesise additional sources of this knowledge when no such sources are necessary to explain it?