[quote=@Hank]
[u][i][b]1)[/b][/i][/u] "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. 

[u][i][b]2)[/b][/i][/u] "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." 

[u][i][b]3)[/b][/i][/u] 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]. 

[u][i][b]4)[/b][/i][/u] EDIT: Not to mention the fact he's just been conscripted. 
[/quote]

I) They are of the Officio Prefectus. Your interpretation of that quote is incorrect. While the Commissars attached to the Militarum Tempestus are part of it, those attached to the Guard have no relation to the Militarum Tempestus.

II) they have no official relation but a Ministorum Priest can still hack your head off if you kill a member of the Militia, and make up a bullshit excuse, and in theory the Ecclessiarchy is the most powerful organization, so the Priest will always be right.  

III) no he is not

IV) Where did you get the idea he was conscripted?