Well, that was sweet of them. The song is great as a song. Poets and historians have separate lanes.
Shakespear’s histories are also inaccurate, flattering the monarch in power and calumnising the monarch who was recently deposed.
Not many inspiring ballads about plumbers for example. Or snow plow drivers.
So when one does come along it is nice.
And you are right about Shakespeare. If you study his plays as propaganda you see whole new layers. Macbeth for example. Do not want to upset ol James by suggesting his ancestor's coup was not legitimate.