The Influence Character can be any of the overall story characters such as the guardian, antagonist, sidekick--even the protagonist. The Hollywood tradition is to make the Influence Character someone other than the antagonist, typically the guardian character (such as Obi-Wan Kenobi in the original Star Wars).

The Influence Character is the character that has the most impact on the Main Character with regards to the MC's personal issues. Therefore, the IC tends to be someone who can get close to the MC. If the MC is also the protagonist and the IC is the antagonist, their roles in the Overall Story make it difficult for an author to design personal interactions that aren't overshadowed by the protagonist/antagonist relationship. That is why the IC is usually NOT the antagonist.