I think SAP is referring to an external entity having an influence on a government's judicial process, not necessarily strictly private. Whether it's the US Government or a special interest group. Assange's case included.
I don't think that is the intended statement at all. Please reread this sentence:
> There's several cases, most notably Assange and [...] that indicate that private entities are putting pressure on governments, who in turn put pressure on their peers in other countries.