So, you point out the contradiction between the title of the section and the section's contents, yet refuse to acknowledge the contradiction?
Of course it's wrong to use the term "British Monarch" in a context outside of or above the United Kingdom; it sets up a contradiction within Wikipedia wherein some articles say (rightly) that the Monarch is shared equally, yet other articles attach the monarch predominantly to one country.  Perhaps it's the fact that you're not from what more than a few editors here seem to still view as "the Colonies" that prevents you from understanding the problem with this.
It's not as though it's a big deal to right the wrong; it's only those with a republican bent (JDM) and those with a imperial pro-British attitude (Thark) who cause a problem when the UK is made to be - horror of all horrors! - equal to the other Realms of the Commonwealth.