They said they don't take statements for that.
Correct. That's not how things work.
If a formal complaint is made to Police, they will take a statement and then decide on what action to take based on the evidence available. The point is, that the decision to take action is made by the Police, not the person giving the statement.
In other words, there is no "just get it on record" approach. If you want to have your side of the story "on record", then you have to make a formal complaint so that your statement has context. Without a complaint, the statement means nothing and is a waste of everyone's time.