You're looking too much at the details while forgetting that the Coalition as a faction was established not by Discovery in terms of what it does but by Starlancer. It is mostly a complete import from that game, but it has also adapted itself somewhat well-ish, with maybe the exception of its playerbase.
That the counterargument to my statement is just a what-if is not something I am keen to entertain, as I only mentioned what the overall view of the group thus far seems be, that being of a very very questionable entity with even more questionable iconography.
We of course can go on for hours and hours listing what-ifs, but the fact of the matter is that this faction as it currently is does not fit either in the inRP universe, nor outside of it in the forums.
As a closing note on the Coalition shenanigans, they have been brought to the attention of the staff many times before with little actual success, so it is only logical then to assume that the emblems they use are fine, short of posting pictures of Lenin and Stalin all over the forums (those got deleted if I recall correctly).