No they are not lying. They might be reporting their rank on a level. Oh wait, I just thought of something. When you click on your profile picture, it does come up with some information. They might be referring to their weekly profile ranking. I completely forgot about that until now!
Go into your game and click on your profile. There should be 3 tabs: rank, current level and levels this week. The rank tab does give you the ranking and I apologize for not realizing it sooner. If you look at your profile picture there is a frame with a number on it. That number will transfer into the rank tab. So the higher the number the closer to the top you will be. The current level tab shows your current level in comparison to other players but when I just looked at my current profile most of the players listed are in the USA so that's what I meant about world-wide. The third tab will compare how many levels you completed in a week compared to other players. Might be the same thing that it's not listing world-wide but you can get some ranking from this.
I did a Google search a couple of times when players asked me about it and there is no data collected from King. I even suggested that they start collecting the data but they never wrote back. I have no clue how they could have written that but then like you said at the beginning maybe they were just making it up to feel good about themselves. If you do ever find a world-wide rank can you please write here and tag me. Then I will have it available for other players.