calling a setReadOnly() on file or directory having 777 permission removes the write permission but leaves execute permission intact.
r_x r_x r_x

Tried on RH Linux Advanced Server 3.0 and Solaris-9 using Tiger-rc Build 63

How to reproduce the stuff:-

create a sample file say check.txt
give 777 permission

compile and execute below mentioned code:-
import java.io.*;
import java.util.*;


public class Test4 {

    public void check() {
      try {
           File file = new File("check.txt");
           System.out.println("Going to make it read only:"+file.setReadOnly());
                          
      } catch(Exception e) {
           e.printStackTrace();
      }
    
    }


    public static void main(String args[]) {
       Test4 ref = new Test4();
       ref.check();
    
    }

}

After executing check the permission on check.txt file using ls -la