so we have to surmise that at some point in the game (and BB missed this ) BP and Nathan (2 of the most honest HMs) made a pact to have a fake relationship to help them win
or
They both are subconsciously on the same unspoken page that they will do this and are doing it even though id imagine EVERY friend and relation would dissaprove
or
its a normal romance that always happens when you stick people together like this just as it happens in EVERY large office in Every town and city in the UK
I know which one sounds more plausable to me