Notice that even in your supposed "refutation" you actually prove my point. Thanks.
Two elements are required for criminal conspiracy: knowledge that what you are planning is a crime, and involving at least one other person.
Burke could not knowingly participate in a conspiracy as a nine year old. In our law, we accept that children do not understand crime.
Later, he could not be indicted for conspiracy unless he reinforced the obstruction with someone else. Both elements must be present at the same time.
You aren’t really going to try and make the case that he didn’t know????
And his parents were the “others”.