Just from personal experience, Android always reports my display as consuming the majority (around 60%-70% usually) of my battery, anytime I've cared to check. That's for general usage as a phone/music player.
YMMV of course, but 70% screen consumption seems way high to me.
In other words: chances are that you only check power use when your display is on. If the display is off 80% of the time and all other components stay on full time, that would sink the power use of the display to around 25%-30%.
So if for a given usage pattern the screen does consume 60+% (which is what I often see) then keeping it off all the time certainly helps ... but also makes the phone a lot less useful!
If I disable WiFi, then check the power consumption, WiFi still appears to be consuming approximately 4% of the batter compared to 42% by the screen, which is the top listed item, and dwarfs the number 2 item, Android OS at 9%.
If I run without WiFi for a period of 24 hours or so, then presumably the WiFi battery consumption would drop to 0%, or at least begin approaching 0%, but either way, this is a far different test than just seeing if the refrigerator light is on.