"Independent of the conventional Imperial Guard Hierarchy, Commissars are instead attached to the Departmento Munitorum's Commissariat and are formally part of the Militarum Tempestus."

There are plenty of examples of Commissars executing members of other military branches (like various PDF's) in disciplinary matters in the fluff of 40K. And you forget that Frateris Militia are technically civilians. 

"The existence of the Frateris Militia is tolerated due to the fact that they have no formal connection to the Ecclesiarchy: they are no more than faithful Imperial citizens eager to prove their dedication to the Imperial Cult." 

Thus, based on your own reasoning, John is totally subject to the authority of a Commissar. 

Source: the [url=http://wh40k.lexicanum.com/wiki/Main_Page]Lexicanum[/url]. 

EDIT: Not to mention the fact he's just been conscripted.