You should at least be able to try to do it covertly. You are after all meeting with minor nobility and wealthy merchants, in their private houses.
The text says: "You spend your bribe money, and are admitted to the mansion of a wealthy merchant and his family and business partners. You sit down in an elegant parlor with your host and his friends, and talk with them for 6 hours."
If you manage to convince these people of the justness of your cause, and they accept your bribe, then does it not make sense that they would not want this fact known by the authorities? Few politicians publically admit that they are influenced by a free-spending lobbyist; rather they all claim to have come indepentantly to the conclusion that Keplerstan is really a great friend.
I could see the case that it should not always succeed at being covert. The game already has various levels of success ("Your tongue is silver tonight", "Most of your audience is unimpressed", etc). When the action fails, then it could become public, but the successful ones should not.
To compare to the action of a priest is unfair. Priests, by definition, preach in public. That's also why it is free: believers don't ask for bribes!
