I just cant understand why it is forbidden to bribe others or offer rewards.
In general, it's not.
When it comes to the IR—tournaments, activity, class, and unit type—it is forbidden to attempt to influence people's decisions from a position of power. Since power comes in many forms, that means it's not just aimed at rulers and council members, but anyone who attempts to exert influence in the realm.
The IR about tournaments is primarily to ensure that
all players, no matter their realm or level of play, have an opportunity to interact with players outside their own realms. Most of the rest of the time, players who aren't in multinational guilds or in council positions do not get that opportunity.