> how is the blockchain under the purview of the us govt?

Likely some inter-state commerce clause that gets used to bring many things under the purview of the feds. It may be more appropriate to ask how it was supposed to not be under the rule of law?

> these were transactions submitted to a blockchain created for the sole purpose of not being controlled by the government

Simply creating a blockchain with that intent in mind seems to be no more effective than a sovereign citizen ranting to a LEO that they are 'traveling by conveyance' in their car and thus not subject to traffic laws.

The fraudsters are American so the US Government certainly has jurisdiction over their actions. Blockchain doesn't really matter to that.

The brothers did the act while in the US, so they're still under the jurisdiction of the US legal system. You can agree by contract to have contractual disputes handled under a certain jurisdiction, arbitration, or within the contractual agreement that defines all rights in a dispute, but you can't just will yourself out of criminal legal culpability by saying that no laws apply to you, even if the victim also were to say no laws should apply. Think about it from another practical perspective: if immunity from laws could be granted by the victim of a crime, imagine the pressure criminals would put on victims to state that they consented to the crime.

They did decide they’re entitled to taxes on transactions..

I bet this indictment will be used as a case study to justify the need for government oversight and taxation.

All fraud conducted in the US or related to the US in any way is under the purview of the US government. The specifics of how it was done doesn't really matter.