Because she doesn't trust the captain not to tell his closest men. Because, as far as he's concerned, this is just something to further her own agenda, and telling one or two of his closest men that he knows won't talk, would be helpful to him. However, a message from the head of the Ordo Hereticus is something that you follow to the exact tee if you value your lack of being on fire.
If she doesn't trust the captain, why did she just hand the note over to a random Space Marine on the steps of the cathedral without confirming his identity first? Her cover identity has now been compromised, rather than simply presenting herself as a Commissar until such time as she could gain a private audience to reveal herself properly.
The Inquisition holds no sway over the Adeptus Astartes, they they completely separate organisation who cooperate due to ancient pacts of support given at the time of the First Founding. A High Lord Inquisitor would have no additional authority to give orders to a Lamenter than a Lord Inquisitor would have. They'd both basically be asking the Astartes to do the Inquisition a favour and help them out.
The note is addressed to 'Commander at Hive City Acane', which would mean either the commander of the local PDF or the civilian governor, depending on the local hierarchy, but has no bearing on the Space Marines. She appears to be trying to use a specific order as a carte blanche to requisition any assistance she can, something which as a Lord Inquisitor she could do anyway.
Why would the Space Marines accept a note without any form of identification instead of a far more secure electro-tattoo? It's possible this piece of parchment is either a forgery or that it's been taken from the original owner. Verification of the document would be required before it could be of any use, and that would take time, communication with the office of High Lord Inquisitor Fyodor Karamazov and would increase tensions between Marian and the Marines which could've been avoided had she simply introduced herself as a Commissar.
If she'd just flashed her tattoo and said "Inquisition business" the Marine would've simply accepted her authority until such time as she proved a threat to the sanctity of the Chapter, with no further explanation of her actions required.
Don't worry too much about all this though, I'll have Quintus look into it when he arrives at the meeting shortly. :)
