Direct from the letter in question (underlines added): "Notwithstanding his life of national service, the media are awash with unfounded allegations, outrageous claims of treason, and vicious innuendo directed against him. He is now the target of unsubstantiated public demands by Members of Congress and other political critics that he be criminally investigated. No reasonable person, who has the benefit of advice from counsel, would submit to questioning in such a highly politicized, witch hunt environment without assurances against unfair prosecution.
This is the actual wording in the letter. Nowhere is immunity mentioned and certainly no reason was given that even remotely sounds like it is the Trump admin that he fears. Look at the underlined text again and ask who is he afraid of? Who could possibly be responsible for unfounded allegations, outrageous claims of treason, and vicious innuendo. Who could he be possibly referring to in this statement; unsubstantiated public demands by Members of Congress and other political critics that he be criminally investigated.
Not exactly the context that is being reported in the media. Read the raw material i.e. 'the actual letter' from his lawyer. Determine what you think it means. Don't rely on CNN, MSNBC etc. to summarize their definition of what the letter meant. That isn't taking responsibility.
