I'd be willing to bet that we misunderstand those arrows. My most recent interpretation of them are that they indicate which way that factions' change in influence is headed. Not an indicator of our relationship with that faction. Remember, in Elite, it's not all about us.
Don't mistake reputation and influence. They both have their own tab in the Status screen. Reputation is your relations with the factions and is listed under the Reputation tab and that is subject to decay, influence is how much power the factions have within the system, and that is listed under the System Status tab.