> And you certainly don’t want an agency asset floating around in the legal/prison system of another country, friend or foe.

This person was allegedly looking at CSAM.

Police and courts interrogating someone as to why they were looking at CSAM is a specific line of enquiry and doesn't touch upon their job.

Also from the US State Department website:

    Under international law and practice, persons enjoying immunity from the jurisdiction of a receiving State’s laws nonetheless have a duty to respect those laws. Immunity is not a license for misconduct. It is a doctrine intended to benefit the sending State or IO, not individuals. 

If the allegation is correct and the guy was looking at CSAM at home, then that has zero to do with their job and therefore it is as per the State Department paragraph above, i.e. the doctrine does not apply. Allegedly looking at CSAM at home does not "benefit the sending state".