About illegal material: I've read there were already illegal pics and links stored in the blockchain, since 2013 or so:
https://www.coindesk.com/markets/2018/03/27/child-porn-on-bitcoin-why-this-doesnt-mean-what-you-might-think/From the article:
Princeton professor Arvind Narayanan tweeted that the mainstream media's response to the report was "unsurprisingly superficial," adding, "First, the law is not an algorithm. Intent is an important factor in determining legality."
[...]
Plus, every U.S. state's handling of the disseminating of illicit material is different, but recalling Narayanan's sentiment, most laws hold people accountable only if they knowingly possess or produce, sell, broadcast or access the content with intent to view.
If that's the case, they should easily be able to back their statements by posting the block hashes. Knowing how media operates when it comes to Bitcoin and crypto, it would not surprise me if they stated it as fact, just because someone told them it is theoretically possible, or if it happened on another chain and they just attribute it to 'Bitcoin', because that pulls more views.
Generally, claiming anything being stored on the Bitcoin blockchain is one of the easiest things to prove; it is much harder to prove something like the correctness of a cryptographic algorithm or the existence of certain data on some company's server. As the ones putting out such accusation, they should also provide the proof.
Furthermore, if it was the case that someone already uploaded illegal material, we all know that it is not trivial to upload whole files into the blockchain. Technical users here may know how to do it, but there is no purpose-made application and mechanism
specifically for uploading and forever storing any data to the blockchain, as well as for viewing it.
Only because something is possible, doesn't mean it should be done, and only because it has been done before, is not a justification to keep going and encouraging it. Civilization has done horrible things for centuries, and at certain points in time realized it was wrong and stopped doing it.