I think there's a bit of confusion over the difference between saying AN oath of silence instead of THE oath of silence. It just says 'an oath of silence' meaning they are sworn not to speak specifics of their Deathwatch activities, not that there is a specific oath in the same terms as the DW pre-mission oaths.
This idea is reinforced by Cyrus' dialogue in Dawn of War 2 as well as the recent Deathwatch novel by Steve Parker, so feel free to use or ignore that information as pleases you. DW marines do not speak to others of their exploits in the Deathwatch, but their tactical and strategic knowledge is exploited where possible. For example, Cyrus doesn't say under what circumstances he fought the Tyranid in the DW, only that he did, and then informs his brothers of the kind of threat they pose and to target Synapse creatures. So as I consider it, in returning from the DW, the home Chapter benefits from the warfare knowledge its brother has gained without the sensitive information surrounding Inquisitorial activities being compromised. So, the Chapter may not know about the Necrons buried under world X, but if they stumble on to world X and encounter them, the DW brother who fought them can pipe up with the best ways to kill them.