How do I show up as "invisible" on facebook?

Facebook has been getting really dumb lately. I used to be able to 'turn off chats for all contacts' and voila, I'm "offline". Now they have this new show as active or whatever. I made sure to set it to off on both my phone and computer.(messenger and website.) but people still see me. I have a friend who usually contacts me when I'm on and I asked him could he see me online and he said yes. I have this other guy bugging me every time I log on whom I barely know. We just happen to be in the same group. It's just easier to browse invisible most times.