No, Police cannot prevent anyone who is willingly gives his / her statement – be it factual or contain bundle of lies – the Police has to record the statement as it is. Otherwise, Section 163 of Cr.P.C. deals with a situation as follows;

Bribe [inducement] should not be given by the Police or the person who is in authority to the Accused and or to the witnesses.

The Police or any person who is in authority should not prevent the witnesses or to the Accused in giving their statement at their own will and pleasure.

Note: This provision relates to Section 24 of the IE Act, which explains that in criminal proceeding a confession given by the Accused [to the Police] is irrelevant. And at the same time the confession given by the Accused in the Court under Section 164[4] of Cr.P.C. shall have no bearing effect in this provision.