I can put a tentacle bear with dragon wings on a flag, doesn't mean it exist.
We have no proof that it exists beside the flag.
Sure you could do that. Care to supply a rational, practical reason as to why you would?
Symbols are only valuable if they convey a specific, intended, EASILY UNDERSTOOD message.
The American bald eagle is the national symbol of the US because it is a graceful, powerful animal and the founders wanted that same power and grace to be associated with their new nation.
The Eagle's value as a symbol comes from the fact that you don't need to be educated or even literate to understand the qualities of the eagle. You only need to have seen one hunt, snatch a rabbit from the field or a trout from the stream to KNOW what badasses they are!
If the NCR is looking for an EFFECTIVE symbol to communicate to ILLITERATE, UNEDUCATED wastelanders that they are a powerful force, they need to use a symbol those wastelanders can understand.
If two-headed bears don't exist, they're useless as a symbol because nobody will understand what they mean.
As someone else already pointed out, the only two-headed animals we've seen are brahmin. Brahmin are stupid, docile prey animals. If you're looking to makeup a power symbol you would not use two heads because two heads would make most wasterlanders think of stupid, prey animals NOT powerful predators.
I'm sorry but there is no good reason to use the two-headed grizzly as a symbol unless they actually exist as big, scary predators. Otherwise, wastelanders would just look at the flag and think, "Wow, those douchebags really svck at drawing brahmin. Let's kill 'em and take their stuff."