It's actually the other way around. There's no such thing as globular maps. Any globes you see are simply globular projections of a flat earth.
And why on (flat) earth would they do that?
The whole point of maps being flat is they are easier to work with and navigate by than carrying a globe around, but because the earth is a globe any map has to be a projection. If the earth were really flat then a map would represent it without any projection, globes would be completely pointless and superflous.
Do you believe the UN would choose an inaccurate map as their primary logo?
I believe that a logo is 2D and in choosing a logo which represents the whole earth they picked a 2D projection of the globe. There is no "accurate" projection because it is not possible to represent a globe correctly in 2D. Do you believe that the UN logo accurately depicts the layout of the flat earth and matches flight times and routes?